Great question. Except you have chosen "stepbrother" which would be the son of a stepmother or stepfather. If you mean did he have a brother in his adoptive family whose mother was Hatshepsut (the woman who adopted him) and father was Thutmose II (the husband of Hatshepsut) then the answer is "No", definitely not. But he did have a half-brother, whose father was Thutmose II, probably many, born from lesser wives and concubines. Thutmose III, the Pharaoh when Moses fled Egypt, was one such half-brother.
Amenhotep II, the Pharaoh of the Exodus, was Moses's nephew, or if you like Moses was his half-uncle (if there is such a term) by adoption.
I don't often think of Moses as being the adoptive son of Thutmose II because Hatshepsut's adoption of Moses was probably a power play by her against her husband, Thutmose II, and his sons by other women.
But still, here is the legally correct situation: Hatshepsut was (probably forced to be) married to Thutmose II in order to strengthen his claim to the throne. So Thutmose II was the husband of Moses adoptive mother and so Moses's adoptive father. Thutmose II had concubines and less important wives and Thutmose III was the first son of one of the minor wives called Aset.
So, remembering that all these relations are because of Moses adoption, Thutmose III was a half-brother, with Moses's adoptive father Thutmose II as the actual father of Thutmose III, (but who did not have Hatshepsut as mother). Thutmose III was Pharaoh when Moses had to flee from Egypt. When Moses returned to Egypt to deliver freedom to the Hebrew slaves Amenhotep II was Pharaoh, who was Thutmose III's son. So Moses would have been Amenhotep II's uncle. Amenhotep II was the Pharaoh at the time of the Exodus.
But, and here is a big BUT. When Thutmose II died 1504 BC Moses would have been 22 years old or so. Thutmose III would have been much younger, even in his infancy: we know this because Hatshepsut was chosen to be a regent to help him until he reached adulthood. So when Thutmose II died Moses did not become Pharaoh: rather, Thutmose III became Pharaoh and he was younger than Moses.
Two possibilities follow: either
A) Thutmose II NEVER ADOPTED Moses as his legal heir. The adoption of Moses was Hatshepsut's idea, and not his, and he never recognised Moses as his son. Or, probably more likely,
B) Moses WAS Thutmose II adopted son, but when the time came for Moses to be made Pharaoh upon Thutmose II's death, Moses refused.
The problem with option "A" is that the reign of Thutmose II was authenticated by his marriage to Hatshepsut, (as explained below). Would he have dared to contradict her by refusing to recognise a son she had adopted? It seems unlikely. And scenario B fits better with the Scriptural description of Moses's refusal of "all the fleeting pleasures of sin" in Egypt (Hebrews 11:25).
The whole period is quite fascinating and I hope you will let me show you why.
Sorry the full answer below goes a long way from your question but I hope you find it interesting nevertheless.
Moses was adopted by Hatshepsut who later became (a co-regent) Pharaoh herself (alongside Thutmose III). Hatshepsut married her half-brother Thutmoses II and bore only a single daughter called Neferura. It is very likely that Hatshepsut’s plan was that Moses would marry his sister Neferura and become Pharaoh, giving Hatshepsut a position of power as Moses’s (adopted) mother, and the actual mother of Neferura, the Great Royal Queen.
If you read all of this I think you will see there are hints of intrigue and power struggle in the royal family of Egypt which are complemented by the account in the book of Genesis.
Firstly though, it is unfortunate that Wikipedia and other online sources adopt the Low Chronology for the 18th dynasty and do not even indicate there is a High Chronology. The two chronologies differ by 25 years. Albeit with some debate, the two chronologies are equally possible. I adopt the High Chronology here because it fits perfectly with a few points in the Biblical account. The High Chronology and the Low both rely on an astronomical observation of a heliacal rising of Sothis. The High assumes the observation was made at Memphis, the Low assumes the observation was made at Thebes. (See the articles referred to below for more information.) Here are the regnal dates for the two chronologies:
First reigns of the New Kingdom
Ahmoses I....... 1575-1550.... 1550-1525
Amenhotep I. 1550-1529.... 1525-1504
Thutmose I.... 1529-1517.... 1504-1492
Thutmose II.. 1517-1504.... 1492-1479
Thutmose III. 1504-1450.... 1479-1425
Hatshepsut..... 1498-1483.... 1473-1458
Amenhotep II. 1452-1425.... 1427-1400
This is the family tree of the Pharaohs of the early 18th dynasty. It would be useful to produce a family tree diagram of the following as you read it:-
Ahmose I, the first Pharaoh of the New Kingdom and 18th Dynasty, had at least two children by the Royal Queen Ahmose Nefertari (also given the title “God’s Wife of Amun” which was passed down to Ahmose-Meritamun and Hatshepsut): the children were Amenhotep I and daughter Ahmose-Meritamun. Amenhotep I probably died childless, and chose Thutmose I to be his successor. He was married to Ahmose. It is possible Ahmose was a daughter of Ahmose I. Queen Ahmose gave birth to Hatshepsut (and another daughter Nefrubity, and two sons who died before their father). Thutmose I also had concubines/lesser wives and one of these, Mutnofret, gave birth to Thutmose II. Hatshepsut was given in marriage to her half-brother Thutmose II and she gave birth to Neferura. Thutmose II married other lesser wives and one of these, Aset, gave birth to Thutmose III. Neferura was given in marriage to her half-brother Thutmose III but if there was any offspring they did not become Pharaoh or marry any Pharaoh. Thutmose III also married Queen Meritra-Hatshepsut who gave birth to Amenhotep II. One of Amenhotep II's wives gave birth to Thutmose IV who cryptically explains how he came to be Pharaoh in an inscription called the Dream Stele (at Giza) – i.e. it was unexpected he would become Pharaoh.
(Interestingly Amenhotep II was buried in Tomb kv35 in the Valley of the Kings. When his tomb was excavated in 1898 by Victor Loret it contained along with the mummy of Amenhotep II, still in its sarcophagus, the bodies of eight other named pharaohs, three unnamed women and an unnamed young boy. - See: Ian Shaw & Paul Nicholson; in entry under "Amenhotep II", page 29. One wonders if the boy was a son of Amenhotep II.)
If you draw this out into a family tree it will be clearer. From the family tree it becomes clearer to see that both Hatshepsut and Neferura were (most probably) of the royal line proper, i.e. descendants of Ahmose I; but Thutmose I, Thutmose II, Thutmose III, Amenhotep II and Thutmose IV were certainly not.
You will notice that Hatshepsut became co-regent with Thutmose III in 1498 BC. At first she was appointed regent (to assist the Pharaoh) because of the infancy of Thutmose III but later she became joint Pharaoh alongside Thutmose III. Militarily Thutmose III was immensely powerful. Hatshepsut’s power base lay with the religious establishment, the priests, especially the priests of Amun, and the knowledge that she, and not Thutmose III, was truly of the royal line.
Hatshepsut had a chief steward called Senenmut who entered royal service in the reign of Thutmose II. I quote from Ian Shaw and Paul Nicholson’s book British Museum Dictionary of Ancient Egypt (1995): “Under Hatshepsut he [Senenmut] became the most influential member of the royal court.” “His numerous titles included the role of steward of Amun and tutor of Hatshepsut’s only daughter Neferura.” He has many surviving statues, some of him with Neferura as a child sitting on his lap. “He built two tombs for himself,” the first one he completed, but the second grander one was “never completed, and, like the images of Senenmut at Deir el-Bahri and elsewhere was defaced in antiquity. This defacement was probably caused by some kind of fall from grace, since there is no further record of Senenmut from late in the reign of Hatshepsut.” (He is last attested in the year 1485 BC.) “Neferura is [also] not attested after Hatsheput’s eleventh regnal year.” (1487 BC)
It should be remembered that Hatshpesut’s statues were also defaced in antiquity.
To get the date of the Exodus from Egypt and the date of the birth of Moses you need to take note of verses 1 Kings 6:1, and understand the confirmation of the date indicated by 1 Kings 6:1 given in Ezekiel 40:1 and Leviticus 25:9.
1 Kings 6:1 says:- “And it came to pass in the four hundred and eightieth year after the children of Israel were come out of the land of Egypt, in the fourth year of Solomon's reign over Israel, in the month Zif, which is the second month, that he began to build the house of the Lord.”
The date of the reign of Solomon has been established by several independent studies: including William H Barnes look at the Tyrian King Lists in “Studies in the Chronology of the Divided Monarchy of Israel”, and Edwin Thiele’s discovery of the meaning of the dates in 1 and 2 Kings and 1 and 2 Chronicles. (See the articles named below.) The Temple of Solomon was started 967 BC. 1 Kings 6:1 says it was started 479 years after the Exodus. So, according to this the Exodus happened in 1446 BC.
Independent of this is Ezekiel 40:1 and its explanation in the Seder Olam and the Talmud. The Seder Olam was written by a Jew in the first century AD. The Seder Olam says that the Jubilee of Ezekiel was the seventeen Jubilee year. Ezekiel 40:1 should be translated thus “In the twenty fifth year of our captivity, on Rosh Hashanah (New Year’s Day), on the tenth day of the month, in the fourteenth year after that the city was smitten…”. Rosh Hashanah happens in the autumn after the last harvest of the year. It begins the agricultural new year. There is a special year every 49 years called the Year of Jubilee. In a Year of Jubilee the year began on the Day of Atonement on the tenth day of the month (Leviticus 25:9,10); in all the other 48 years New Year's Day fell on the first day of the lunar month (of Tishri in autumn). What Ezekiel is saying is that the year mentioned in Ezekiel 40:1 was a Jubilee Year. The Seder Olam says it was the 17th Jubilee. The year can be established as 573 BC (from the year of the fall of Jerusalem), and so the entry into Canaan (when the Jubilee cycle originally began) can be dated to 573 BC + 17*49 = 1406 BC. This was exactly 40 years after the Exodus date indicated by 1 Kings 6:1. The Bible says there were 40 years of wandering in the wilderness after the Exodus.
So 1 Kings 6:1 and Ezekiel 40:1 (together with Leviticus 25:9,10) agree.
Essentially, there are two independent witnesses that the Exodus happened 1446 BC.
The Exodus happened when Moses was 80 years old. So Moses was born 1526 BC. This is the first interesting date if we choose the High Chronology. It will be remembered that Moses was hidden when he was born for fear he would be put to death. But Aaron was not hidden. Why not? Clearly Pharaoh’s command to kill the baby Israelite boys had not yet been issued when Aaron was born. Now Aaron was born three years before Moses (Exodus 7:7). Such a command most likely would have been issued when a new Pharaoh ascended the throne. Under the High Chronology, Aaron was born at the end of the reign of Amenhotep I. The dates suggest that when Thutmose I ascended the throne he may have been the one to issue the order to kill all the baby Israelite boys. The rule over Egypt by the foreign Hyksos was still a recent historical event for the Egyptians.
When Moses was 40 years old he embraced his Israelite roots (Acts 7:23). This was in 1486 BC. At this time, according to the High Chronology (but not the Low) Thutmose III was Pharaoh. Moses, having been taught by his mother he was himself Israelite, took sides with the Israelites and against the Egyptians, and killed an Egyptian officer. Pharaoh Thutmose III heard and sought to slay Moses (Exodus 2:15) so Moses fled. The opportunity had been taken by Thutmose III to try to kill Moses because Moses was a potential threat to Pharaoh's position: Moses had a legitimate claim to the throne.
When Moses was 80 years old (or nearly 80) the LORD said to him “All the men are dead which sought thy life” (Exodus 4:19), because he was 80 years old when he stood before Pharaoh (Exodus 7:7). The most important person seeking to kill Moses was Pharaoh himself (Exodus 2:15). So we need to find a Pharaoh in the relevant period who reigned at least close to 40 years and probably more. During the whole period from the beginning of the 15th Dynasty (1650 BC) down to the end of the 20th Dynasty (1069 BC) there are only two Pharaohs who reigned for 40 years or more: Rameses II who reigned for 66 years (1279-1213 BC) and Thutmose III who reigned for 54 years (1504-1450 BC). [What Exodus 4:19 is saying is that the long-reigning Pharaoh, who ruled in 1486 BC, died before Moses returned to Egypt in 1446 BC. So neither Thutmose III nor Rameses II could have been the Pharaoh of the Exodus itself for this reason alone - it would have been the following Pharaoh (Merenptah in the case of Rameses II, and or Amenhotep II in the case of Thutmose III).]
Again, according to the High Chronology Thutmose III died 1450 BC, i.e. before 1446 BC, but according to the Low Thutmose III died 1425 BC. Once again, the High Chronology beautifully fits the Bible account, and Exodus 4:19, but the Low does not fit at all.
During the reign of Thutmose III Egypt reached the height of its power, which he passed on to his son Amenhotep II. Thutmose III has sometimes been called the Napoleon of ancient Egypt. He raised Egypt to great power. It is fitting that God showed his power over Egypt when Egypt was at the height of its power. In Exodus 9:16 the LORD says “In very deed for this cause have I raised you up that I might show in thee my power, and that my name may be declared throughout all the earth.” God raised up the Pharaoh and Egypt to a height of extraordinary power to demonstrate his own power in overcoming them. David Rohl’s belief that the Exodus happened during the reign of a relatively obscure Pharaoh and a period of relative Egyptian weakness are not credible.
Returning to Senenmut and Neferuri a speculation can be constructed which sounds very tempting. It goes like this:
When Hatshepsut retrieved Moses out of the river as a baby she claimed that Amun had miraculously given her a child. He was not a Hebrew child, he was from the god Amun. Hatshepsut's title was, after all, “God’s Wife of Amun” which was passed down first from her grandmother Ahmose Nefertari, then her mother Ahmose, so it was only natural(!) she should have a miraculous child of Amun.
The priests of Amun chose to believe her and joined in with the illusion because it gave them more prestige verses the priests of other gods. (Also, remember that Ancient Egypt was essentially a land of a cult with the Royal Family at the top of the pile, rather like North Korea today, and failing to believe those in authority had serious negative consequences, just like any other cult today.)
Hatshepsut had a plan: Moses would marry her daughter Neferuri and she would then have a much more secure power base herself. But, unfortunately for Hatshepsut, Moses refused at every opportunity. When the opportunity came to marry Neferuri, Moses refused. When the opportunity came to become Pharaoh, Moses refused. As long as Thutmose III was alive her own power was limited. Her plan then was to finally persuade stubborn Moses to agree and then to assassinate Thutmose III and then Moses would marry Neferuri and become Pharaoh. Hatshepsut’s chief servant/advisor Senenmut knew/advised this plan. Neferuri might have known about it too, and approved. The priests of Amun might have known as well and approved because it would increase their power too. But Moses carried on being stubborn and refusing.
Finally, in 1486 BC, Moses refused all the pleasures of Egypt and chose to belong to the Israelites, “refusing to be called the son of Pharaoh’s daughter, choosing rather to suffer affliction with the people of God, than to enjoy the fleeting pleasures of sin.” (Hebrews 11:24,25).
The whole plan quickly unravelled: it was now clear to everyone that Moses was a Hebrew after all (as Thutmose III and his allies had long suspected?) and not a son of the god Amun. Someone who knew of the scheming plans of Hatshepsut, Senenmut and Neferuri to get rid of Thutmose III revealed the plot to him. Neferuri soon falls from grace (unattested on any monument after 1487 BC). It takes a little longer to point the conspiracy up to Senenmut, but he is no longer attested after 1485 BC. Finally the conspiracy points to Hatshepsut and she falls from power/is assassinated in 1483 BC.
Possibly after the Exodus many of the statues of Hatshepsut and Senenmut are defaced, and other monuments which had been put there by Hatshepsut are attributed to Thutmose III - all the Egyptians are extremely angry with Hatshepsut and Senenmut because their plan has horribly back-fired: instead of Moses becoming Pharaoh, he has lead all their Hebrew slaves out of Egypt.
The date of the final rejection of "all the fleeting pleasures of sin" by Moses, 1486 BC, fits well with the dates of the apparent falls from grace/power of Neferuri (on or after 1487), Senenmut (1485), and Hatshepsut (1483).
“British Museum Dictionary of Ancient Egypt” by Ian Shaw and Paul Nicholson (1995). (There is now an improved 2nd edition, 2008.)
Google the following:-
For dating the construction of the Temple of Solomon:-
“THREE VERIFICATIONS OF THIELE'S DATE FOR THE BEGINNING OF THE DIVIDED KINGDOM” by Rodger C Young
“The Talmud’s Two Jubilees and Their Relevance to the Date of the Exodus” by Rodger C Young
On Egyptian chronology for the New Kingdom, 18th dynasty:-
“The Present Status of Egyptian Chronology” by WA Ward, jstor, 1992
“Redating the early 18th Dynasty of Egypt” by Ian Onvlee, academia.edu, 4th Aug 2013
“A Re-assessment of the Absolute Chronology of the Egyptian New Kingdom” by R Gautschy, jstor, 2014