If Christ is God and Christ has two natures, one fully human and one fully divine, then Mary could only be considered to be the Mother of the Human Nature of God, the Son. To say she is the "Mother of God" implies that she is not only the mother (progenitor) of Christ's physical nature, but also the mother of his divine nature. To say that Mary is the Mother of God is to say that Jesus' human nature standing alone is God, which would then make God a Quaternity instead of a Trinity. You would have God the Father, God the Word, God the Son (human nature of God the Word) and The Holy Spirit.
Since Mary was not the mother of the divine nature of God The Word, she cannot be said to be the Mother of God. She is strictly the Mother of Jesus. That is the way the Bible refers to her. That is good enough for me. I'm sure it is good enough for her.
That's Nestorianism.
-A8