I find the Catholic title "Mother of God" for the Virgin Mary confusing
It shouldn't be. Let's rephrase 'Mother of God':
Of Whom was Mary the mother?
If you must withold 'God,' then you withold it of Christ who is very God (in addition to be truly human, or vice versa). And would be a heretic: a Nestorian, to be precise.
If you say 'Jesus, in His humanity' you withold 'God' from Christ, which is impossible: He being at all times absolutely God and absolutely man, and never only either, since His incarnation—since the Hypostatic Union.
But when the fulness of the time was come, God sent his Son, made of a
This Son was at all times 'God' and so Mary, being His mother, is indeed the Mother of God. It's really very simple.
And whence is this to me, that the mother of my Lord should come to
Now if one doubts this Lord is Christ, or that He is "Lord..and..God" (John 20:28) Then He has a faulty Christology. As well as a misunderstanding of the doctrine of the Trinity. The doctrine of Trinity is such that each Person of the Trinity is truly God, individually, but not separate Gods. Nonetheless, they are each God because they are of the one substance, God. each Person of the Trinity is not the Trinity; but each Person of the Trinity is God, fully, truly.
"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"
Not if "the Word was God" (John 1:1) is in your Bible.
One needs to make the "the Word" who was and is "God" different from the one "born of [Mary]" (Gal 4:4) in order for her not to be the Mother of God.