The Appelation 'Son'
The meaning of the term 'Son' is central to the discussion: what exactly are we saying when we say that the Son is the 'Son' of God—what kind of relationship between persons does this denote? Moreover, how, if He is the Son of God, is He Himself God: doesn't that imply there are two Gods in view, that they can be distinguished from one another, 'God' and 'His Son'?
In trinitarian Christianity, the 'sonship' of the Son (in contradistinction to so-called adoptive sonship: Luke 3:38; John 1:12; Mt 5:44-45 etc.) denotes the sharing of a nature: 'Father,' 'Son' (John 16:27-29; 1:1b vs. 1:1c; Mt 1:23b).
What do 'Father' and 'Son' as non-uninterchangable appelations mean? Simply that one gives (in the eternal, rather than temporal, sense) the divine nature—'to be the one God'—to Another. Thus the former is called a 'Father' and the latter 'Son.' So it has nothing to do with the 'oldness' of the Father, or the 'recentness,' as 'newly begotten,' of the Son, since they are eternal, but rather a statement of fact about the relationships within the one God from all eternity. It also means the Son is God in this very sense: has the nature of the one true God (John 16:15).
So He isn't separate from God, but is definitional to God.
How, then, is He not a separate God, if He is the Son of God, yet Himself God?
First, I would note that it isn't a trintarian invention to both differentiate the Father and the Son and yet affirm their both equally being God. Scripture clearly does so:
John 1:1 In the beginning was the Word, and the Word with God, and the Word was God.
In Greek it's clear what is being attributed to the Word/Son here:
- Was already present when the beginning came about (v. 3): εν αρχη ην
- Was with God (the Father: v. 14): ην προς τον Θεον
- Was Himself God: και θεος ην
Ergo, necessarily, there is distinction of Persons within the one God, because we only believe in one God.
Second, trinitarians don't assume that God is unipersonal (there being one God tells us nothing extra about the one God).
Thirdly, and in answer to the abovementioned question, as you may have deduced, 'God' in 'the Son of God' John 1:14/'Word of God' Revelation 19:13 referes to none other than the Father. This is why we find Scripture referring to the Father as simply God, and the Son and Holy Spirit usually in terms of Him: because this reflects the ontological dependancy of Son and Spirit upon the Father for existence as God.
Trinitarians can even say that the Father is "the only true God" (John 17:3) Why? Because to be God, whether the Father or Son, is to be the only true God (there isn't a way to be God while not being the only true God!). After all, why would the Father not be able to be called 'the only true God' in trinitarian theology? If the Father is God, and to be God is to be the only God because there are no other Gods, then the Father is the only true God. But this applies to anyone who is God, even the Son and the Holy Spirit; it's not exclusive, in otherwords, of God the Son, God the Holy Spirit.
TL;DR the 'God' in 'Son of God' doesn't indicate 'this thing over here which is exclusively God which this thing over here is Son of' but rather the opposite: that the Son shares the nature of the Father, who is also God. They are the one God, because God is not Unitarian and doesn't anywhere claim to be.
A Word about the Ineffability of God in General
'Son' especially does not denote a literal begetting of offspring (as though the Son were the product of a divine sexual act)—'beget,' 'Father,' 'Son' are anthropomorphisms, as God doesn't create audible Words when He 'speaks,' with His 'mouth,' nor does He literally, sexually 'beget;' they rather describe, by analogy with human experience, something about the divine nature which otherwise is utterly incomprehensible.
When "the Word became flesh" (John 1:14) He, to become a true and not ficticous man, took on a real human nature free from sin, and so exposed Himself to the limitations of men. But personally ('who is that man really?') He is the eternal Word (John 8:58 "...Before Abraham as, I am") in the flesh. That's why we can even say that "the Lord of Glory" and "the First of the Last" was crucified and killed (1 Corithians 2:8; Revelation 1:17-18)! Because 'God died and doesn't exist anymore?' No, because He who is personally God, not a human person, and took on a human nature, did in that human nature. It's also why the Church has always recognized Mary as Mother of God (Θεοτοκος), because the One she bore is God—it began as and continues to be a Christological (more so than Mariological) doctrine.
Philippians 2:5-11, given as an exmaple by St. Paul of immense humility, shows us a few things:
- The preincarnate Word, later to be called Jesus when He was born as man of Mary, had equality with God He set aside out of love for us, not by changing His nature, but in that He took on a lesser one.
- He is exalted by God even as man, so that at the name of Jesus every tongue confess etc.—a passage taken straight from the Old Testament and clearly in reference to the only true God, and applied to Jesus, because He is God in the flesh. When the Son is 'given' something He doesn't have, it is only in that He is man. E.g John 17:5.
I hope your question is answered somewhere in there.