“No, Mary is not God’s mother.”
Jesus is God. Mary is His mother. Mary is the mother of God. She is NOT the mother of the Trinity.
The mortal human Mary gave birth to Jesus, who was God become Man. She really has no more important significance in Christianity other than that.
I’d add…Elizabeth, moved by the Holy Spirit, asks, “How is this, that the mother of my Lord should come to me?” Elizabeth was the wife of a Jewish priest, and the daughter of a priestly family. What else, exactly, would she have meant by that?