Is Mary, "Mother of God," the mother of the Son or of the whole Trinity?

I find the Catholic title "Mother of God" for the Virgin Mary confusing. It is clear that she was the mother of Jesus, the Son. But the title suggests (indeed, not literally, but still) that Mary is mother of God as a Trinity. Is that correct? If so, it creates the problem that a human (or is there reason to say that Mary wasn't (entirely) human?) gave birth to God, while God created mankind. This problem doesn't exist when Mary is only mother of Jesus, because then it could be merely a way of speaking to say that Mary was the one through whom the Word became flesh, which would be the Protestant view as described in https://christianity.stackexchange.com/q/15779/5729