You could say that in Trinitarian thought “is” is not commutative. The Son is God, but God is not the Son ... kinda like that.
So if the Chalcedonian formula and the Nicene formula are taken together, it does not follow that Mary is the mother of the other “persons.”
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The Incarnation is about the eternal entering temporality. God is not before or after. He is. It's risky but I think of him surrounding or “comprehending” time.
So, the problem of a mother having to pre-exist the child is not a difficulty. It IS a wonder. Our Advent Marian hymn, Alma Redemptoris Mater riffs on the wonder:
..., tu quæ genuísti,
Natúra miránte, tuum sanctum Genitórem ...
You who “generated”, nature marveling, your holy “Generator.”
(Hey, I don't write this stuff ... Srsly, we don't have a good English word for “genitor.”)
So, especially if you think of eternity not as time extending infinitely forward and backward but as outside of time, there is not a huge problem with reconciling the way Mary is “before” Jesus and the way she cannot be thought of as “before” God. The Incarnation is God entering the realm he made, the realm of time and change and therefore of before and after.
And there are good reasons for thinking of eternity that way, having to do with the changelessness of God. Time is “the measure of change.” So until there's something that changes, it is hard to imagine what time would be. Yet there would be God. etc., etc., yatta, yatta.
As to coredemptrix and all, it seems to me that every good dogma has the possibility of starting erroneous trains of thought, and parsing out in what way humans are channels of redemption and in what way they can't be has to be left for another time if we're going to pick apart “Mother of God.”
But now I have to go prepare a class on ... the Rosary! LOL!
That you have to go into your explanation illustrates but one of the problems with the Romam Catholic title of “mother of God”.