Jesus is God Incarnate, that isn't even open for debate.
However, the term "Mother of God" is very misleading as it makes Mary out to be something she isn't and God to be something he isn't. The better term would be "Bearer of God" since Mary is not the biological mother of God, nor indeed can be. She only carried God in her womb, she didn't pass on any divine nature to actually create God as would be the case in a completely biological birth such as Jesus' brothers. Mary can be rightly called the "Mother of Jesus" or "Bearer of God".
However, the term "Mother of God" is very misleading as it makes Mary out to be something she isn't and God to be something he isn't. The better term would be "Bearer of God" since Mary is not the biological mother of God, nor indeed can be. She only carried God in her womb, she didn't pass on any divine nature to actually create God as would be the case in a completely biological birth such as Jesus' brothers. Mary can be rightly called the "Mother of Jesus" or "Bearer of God".