Let's try things your way.
Mary is mother of God.
The Heavenly Creator is God.
Therefore, Mary is the Heavenly Creator's own mother.
Here's a syllogism of the same logical form as yours:
Mary is the mother of a fireman.
Sam is a fireman.
Therefore: Mary is the mother of Sam.
As you can see, your syllogism is formally invalid. My example is formally invalid in precisely the same way. Undistributed middle.
My original syllogism, on the other hand, is valid:
Mary is the mother of Jesus.
Jesus is God the Son, the Word Incarnate.
Mary is the mother of God the Son, the Word Incarnate.
Mary is the mother of the Incarnate Word of God, the Incarnate Son of God, i.e., Jesus Christ. She began to be his mother around the year 0 A.D. She did not exist when the universe was created.
Mary is the mother of a man who is also God. The Incarnate Word of God had a human mother, whose name was Mary. God-made-man was the son of Mary. Mary is the mother of God.
Since you blundered with your last attempt to formulate a syllogism, let's see you try to do it again, without botching it.
What of your own? It was apples and oranges, as another (logically) pointed out.
Why did you persist, and now add all the rest of the "additional explanation" sort of thing?
As I pointed out, all of that type of thing can be required, even regardless of which "title" one gives to Mary, herself.
Mother of God, can go too far, as I just demonstrated.
There is logical enough reason to shy away from full-throated exclamation of that term, and still be able to get to place of understanding that is was God Himself, in the form of the Son (the heir, even, as Jesus used that concept in explaining 'how the heavens go' in regards to man) whom willingly gave Himself, for us...even for those whom had cruelly rejected Him.
While "mother of Jesus" also, admittedly enough as a closed phrase, if you will, doesn't tell us much about who Jesus really is, and so also requires additional information & explanation, but not to explain Mary, herself.
Facts not in evidence.