If Mary is not the mother of God, in other words, if the child whom Mary birthed is not God, then one of three heresies necessarily follows, as I pointed out in #1656.
As to God and Father not being identical - are you now separating the Father from the Godhead???
No. The Father is God, but the 'is' is not an is of [Leibnizian] identity. For the Logos is God too, but the Logos is not [numerically] identical to the Father.
Or are you backtracking and saying the Father is only a part of the Godhead and can be separated from the Son? (i.e., component parts of the one unit)
No. I'm not saying that at all.
-A8
Incorrect. Jesus would have been God had he never been incarnated. He was God always. Never wasn't God. Therefore, Mary was not the mother of Him AS GOD. She was the mother of Him AS MAN. He was both. She was the mother of one of those elements and gave it life. His humanness had a beginning. His Godhood did not. The divine part of Christ eternally preexisted Mary so therefore could not have been sired by her.