Jesus and Contingency

Let's assume that God is omnipotent in the sense that he can do anything which is logically possible (so that he cannot create square circles because a square circle is a contradiction). Now it is thought that God cannot do things like make himself cease to exist, or to become contingent. How does this square with the idea that (at least some part of) God became a man. By entering into time and assuming a bodily form, is that not the meaning of becoming contingent? I can anticipate the answer that Jesus has two natures, the human one that is contingent (and does not exist anymore) and one that is divine (which was never contingent), but this seems to me to just split Jesus into a divine part (which was never contingent) and the ordinary human part, so that the Jesus that walked on Earth was an ordinary human, and hence no need fore the idea of the trinity. Any way to resolve this dilemma? Edit: Perhaps to restate: Do we have to accept that God - in his omnipotence, must be able to create the logically impossible, in order to believe in something like the trinity?