Jesus was not born as a human for the role of a God...He was as you say a prophet, a preacher, a priest and a human...Elizabeth did NOT say the mother of God...She said the mother of my Lord...
Mary was not, is not and never will be the mother of God...
Anyone who knows the bible already knows that Jesus was God and man...No one needs to invent a word to add to it to let us know that Jesus was God and man...Especially while adding the word gives a false notion that Mary was God's mother...
We already know that Mary was Jesus' mother and we already know that Jesus is God...And yet we know that Mary was not the mother of God...God was not created in Mary's womb...The 2nd part of the Trinity was not created in Mary's womb...He already WAS...
Jesus is God in the second person of the Trinity. She bore Him in her womb, gave birth to Him, suckled Him at her breast, Changed His little diapers. Yeah Mary is the Mother of God. Just like your mother is the mother of whatever you are.
She became the Mother of God, in which work so many and such great good things are bestowed on her as pass man’s understanding. For on this there follows all honor, all blessedness, and her unique place in the whole of mankind, among which she has no equal, namely, that she had a child by the Father in heaven, and such a Child . . . Hence men have crowded all her glory into a single word, calling her the Mother of God . . . None can say of her nor announce to her greater things, even though he had as many tongues as the earth possesses flowers and blades of grass: the sky, stars; and the sea, grains of sand. It needs to be pondered in the heart what it means to be the Mother of God.
(Commentary on the Magnificat, 1521; in Luther’s Works, Pelikan et al, vol. 21, 326)