There was some controversy over the phrase in the 80's because some minority of manuscripts appeared to omit the phrase which led to some Bible versions removing it or footnoting it. However, earlier manuscripts were found in the 50's that did have the phrase in it which make the later omissions likely scribal errors (mistakes). It has since been restored to the majority of the versions that had removed it because of this find. This is likely the reason why your version is missing it - if it's an older version.
Text Note: Luke 24:52
I will attempt to give you the reason the Greek (and now English versions) have the alternative that you stated.
In the best manuscripts the Greek states
24:52 καὶ αὐτοὶ προσκυνήσαντες αὐτὸν...
Literally this states, "And they worshiped him..."
προσκυνήσαντες is the aorist, active, participle which means it is a variant. The root would be προσκύνέω.
προσκύνέω has a range from "to do reverence or homage by kissing the hand" in the OT Septuagint but in the NT it means "to do reverence or homage by prostration (bowing or kneeling)"; to pay divine homage, worship, adore; "to bow oneself in adoration."
from The Analytical Lexicon to the Greek New Testament William D. Mounce
To your question about the Vulgate:
You translated this as "52 And they adoring went back into Jerusalem with great joy. 53 And they were always in the temple, praising and blessing God. Amen."
This is what the Vulgate states in Latin
24:52 et ipsi adorantes regressi sunt in Hierusalem cum gaudio magno
This translates to "And they worshiped him, and returned to Jerusalem with great joy."
It appears that whatever English translation you are using just did not translate the Latin word "adorantes" to worshiped but it still came close. If we go back to the Greek this is easier to see.
The operative clause is αὐτοὶ προσκυνήσαντες αὐτὸν.
In προσκυνήσαντες the ντ identifies it as a participle (participles are verbal adjectives as in they describe an action happening to someone or something)
The "σα" means that it is Aorist tense (a sort of past tense that means that it happened prior to now but doesn't specifiy time in itself)
The "ες" suffix means that it is identifying the adverb as describing the group (αὐτοὶ, "they").
We also know that a participle must modify something since if describes an action happening to someone or something and if there are only 2 nouns in the whole clause αὐτοὶ and αὐτὸν (αὐτὸν is singular and referring to a "him" and by context we know the him is Jesus) and the participle is plural and the only noun that is plural is αὐτοὶ (them) then the object of the participle (who it is being done to) must be the αὐτὸν (him).
In the translation you quoted above it doesn't make sense to say "And they adoring went back into Jerusalem with great joy." Here adoring is also a participle without an object. What were they adoring? If this were a verb, that is just an action the group was performing, then we would not expect this to be a participle and would have just been an plural, aorist, active, indicative (think time) form (as far as I know that form is never used anywhere in the NT).
There seems to be something missing as it is stated in your Vulgate version (not your documentation of it but an issue with the translation within it). Remember that the Vulgate was written by Jerome using the Greek so the priority should also go to the Greek text which clearly states that "they worshiped him..."
(All emphasis mine)