There is no equivocation occurring in the following syllogism:
Mary is the mother of Jesus.
Jesus is God.
Mary is the mother of God.
The word “God” has exactly the same meaning in the second and third propositions: the Second Person of the Trinity.
The word “mother” has exactly the same meaning in the first and third propositions: ...one who conceived in her womb and gave birth to...
The second premise is ambiguous in the sense that the word, “God” implies the totality of Jehovah, who is one in essence, and three in Person, not just, "the Second Person of the Trinity", and it also implies His eternal power and divine nature.
That ambiguity is also implicit in the third premise so that the conclusion “mother of God” gives the misleading impression that Mary preceded the Eternal God, which is impossible.
Jesus is God, who became man. Mary is the mother of Jesus according to the flesh (Romans 9:5) However, according to His divine nature He did not have a physical mother.
If Mary is the "Mother of God", how then is Jesus a descendant of David as it says in Matthew 1 and Luke 3 and Romans 9:5?
The conclusion of the syllogism is superficial in that it states only a partial truth and consequently it is misleading. If the syllogism added the word, "incarnate" after the word, "God" in both instances I wouldn't have a problem with it because it would eliminate some of the ambiguity.
Scripture itself is much clearer on the subject than the syllogism.
Cordially,