How can Christ's human nature be part of the Trinity if it is not co-eternal with God?
The short answer
Jesus is the eternal Word, eternally begotten of the Father and equal to him. At the Incarnation he took on a human nature, which had a beginning. That does not diminish the Trinity: one divine Person now has a human nature as well as a divine one, without the human ever replacing the divine.
Jesus is the eternal Word, the eternal Logos, eternally begotten of the Father and equal to the Father. When he became incarnate by the Holy Spirit in his mother's womb, he took on a human nature and entered time. His human nature had a beginning.
There is no real problem here. Christ's taking on a human nature in no way diminishes the Trinity: since the Incarnation, one of the Persons of the Trinity simply has a human nature as well as a divine one. It would be a problem if his human nature supplanted his divine nature, but that is not the case and never could be.