That it is necessary to point out as you have in your post that Jesus is a divine person with two natures inextricably combined in a single person, and that no one is suggesting that Jesus received his divine nature from Mary because she could never give him something she never possessed is evidence enough to me that the appellation, "Mother of God" is too ambiguous and misleading.
If you were to say that Mary is the mother of God incarnate, or "God-bearer" as one post earlier suggested I wouldn't disagree with it.
Scripture itself just refers to her as, "Jesus' mother".
"Then Jesus' mother and brothers arrived. Standing outside, they sent someone in to call him. - Mark 3:31Now Jesus' mother and brothers came to see him, but they were not able to get near him because of the crowd. -Luke 8:19
They all joined together constantly in prayer, along with the women and Mary the mother of Jesus, and with his brothers. - Acts 1:14
Cordially,
What must be understood is that “mother of God” is not a descriptor intended to expand our understanding of who Mary is. It is entirely about who Jesus is. If you know anything about Church history, you know that the early centuries were a time of christological crisis: the Church was hashing out just who Jesus is. THAT was what was critical to salvation, and that is why they cared. Mariology has no reason for existence except as an adjunct to christology. Everything about Mary refers us back to her son. “Mother of God” describes who Jesus is. First-millennium Christians understood this just fine, as a pithy, periphrastic descriptor of Jesus. They were not allergic to thinking this way.