If Jesus has two separate natures, a human nature and a divine nature, it seems logical that Mary is the mother of the human Jesus but not of the eternal God. Can I explain how one person has two natures? No, not anymore than I can explain how one God had three persons! So, I accept it by faith.
You have just resurrected a 5th century heresy known as Nestorianism. Women do not give birth to human natures; they give birth to persons. Mary thus carried and gave birth to the person of Jesus Christ, and the person she gave birth to was God.
The Nestorian claim that Mary did not give birth to the unified person of Jesus Christ attempts to separate Christ’s human nature from his divine nature, creating two separate and distinct persons—one divine and one human—united in a loose affiliation. It is therefore a Christological heresy, which even the Protestant Reformers recognized. Both Martin Luther and John Calvin insisted on Mary’s divine maternity. In fact, it even appears that Nestorius himself may not have believed the heresy named after him. Further, the "Nestorian" church has now signed a joint declaration on Christology with the Catholic Church and recognizes Mary’s divine maternity, just as other Christians do.
The hypostatic union of Christ’s two natures is the issue here. No one can explain and it and no one expects you to. However, Mary is still the mother of God since Jesus isn’t split into two parts. Mary gave Jesus his human nature and the Holy Spirit gave Jesus His divine nature. Since Jesus is truly man and truly God, and Mary is his mother, Mary is also the mother of God. This does not make her a God herself, and the concept is perfectly benign and not should not cause issues.