If we understand God as trip part.. a trinity.. she is not the mother of the Trinity ..she is the mother of 1 part of the triune God ..the one we cll the "son of God /the "son of man"
I personally do not have a specific issue with the term "mother of God" but it is too broad a title IMHO
So, fine, “Mother of God incarnate”
Metmom note that the Holy Spirit (through her cousin elizabeth) prompts Elizabeth to say "Mother of My Lord"
In the Bible she is called "Mother of Jesus" -- who is God Incarnate, hence the term Theotokos or Bearer of God is apt -- you can be more precise with Theoensarkonotokos
you know the reason why the term Theotokos is used if you reference Nestorius.