Since I believer that God can not be divided, Mary, mother of God, is too imprecise of a term and does potential damage to the eternal preexistence of Christ as well as the unity of the Trinity. I not only think it is confusing, but think it is wrong to use in that way. Using the precise term (and biblical term) Mary, Mother of Jesus or Mary, mother of my Lord helps one to be precise, lets one base one's Christology on the person of Christ and preserves his unity with the Father and the Spirit as well as His eternal preexistence.
It is true that this may lead to the absurd notion that she pre-exists God, but till the late Reformation no one held to it, and we cannot really be responsible for what Protestants have in their minds.
Consider this: It's those outside the Catholic Church (mostly) who say,"This could potentially cause damage." But WE who actually use the phrase in our conversation and devotions are not confused, and as I said, put it forth as almost a defiant assertion of the mind-blowing miracle of the Incarnation.
Jesus was God. Jesus was born of a woman. The mother of Jesus is as much the mother of God as Jesus was God -- no more, but no less. We claim ALL the implications of the Incarnation and celebrate it enthusiastically and confidently. You don't have to join us, but don't begrudge us our joy and gratitude in the condescension of God.
It's so interesting. Everyone says we don't place enough emphasis on faith or on Jesus, and then tells us we are making too much of the Incarnation. We can't win for losing!
As for me and my house, we will worship the Lord, and give thanks for all His gifts. His mind-boggling mercy endures for ever.