The title "Mother of God" came about in the early church as a way to signify to those that did not believe in the divinity of Christ that Jesus was indeed God in the flesh. So literally, no Mary was not God's mother. But she IS the mother of Jesus ... Emmanuel ... God with us. So in that sense ... yes, she is the mother of God.
Mary is absolutely and in every sense the Mother of God. She is the mother of Jesus, in whom the human and divine are perfectly and eternally joined. She is not the origin of her son’s divine nature — but she is the mother of her son, a unique person in whom the divine nature is present as it has been from the first instant of his conception.
People who backpedal on Mary as Mother of God fail to appreciate that this teaching also is really about who Jesus is, and about God’s love for the world being so intimate and complete that he penetrates it and joins himself to it.