No one is talking about the two natures of the Word incarnate being "mixed". Even in normal parlance, when a baby is conceived is that spoken of as a mixture or as a union? The answer is clear. It appears you are saying that it is beyond God's capability to supernaturally "unite" with Mary's egg (while keeping the natures distinct) in the way we are saying. No, that's impossible. However, it is fully possible for God to zap a baby into Mary's Immaculate Incubator.
Not only that, but God can somehow take Mary's nature and flesh (or something) and be united, but NOT mixed in the person of Christ. How does this happen so as to meet all the definitions correctly? Magic, of course. When you distinguish between "union" and "mixture", magic is a very useful ally indeed. :)
Christ took on Mary's humanity using her flesh. The rest is an enigma. Mary's flesh had two female genes: that of her mother and that of her father's mother. Obviously, the enfleshment of the Word was not incumbent on her genetics. It was her humanity, her human nature, that the Lord assumed.
If the rest is an enigma, then what does "using her flesh" mean? How did it constitute a union, but not a mixture? Is all of this a roundabout way to give Mary credit for Jesus' sinlessness?
Just as Adam did not need human genes to become human, neither did the Word need human genetics to become human. He used Mary's flesh in order to become related to humanity, Abraham and Adam, as well as David and fulfill the prophesy.
Related to humanity means "but not fully human". This makes Jesus' humanity a sham, does it not?
What do you mean Adam did not need human genes to become human? What did Adam use instead to become human? :) Did Adam not have fully normal DNA? What would you say to the idea that Adam did not become human, but rather God created Adam human with fully human genes? Am I way out in left field here? :) Adam's creation was a true "zapping" in this sense. God created every physical thing from scratch (dust). Adam also had no prophesy to meet. If you say that the human body of Jesus was created in the same way, then that makes Mary a surrogate.
Well, a mix of course. Each haploid carries specific mix of genetic codes, and each fertilized egg results in a unique mixture of genetics material giving rise to a uniuqe person. Union is simply two parts stuck together, still distinctly separate entities.
My example with Adam was to show that God doesn't have to use the "conventional" method of (pro)creating humans, not that Adam was somehow without a genetic code.
but God can somehow take Mary's nature and flesh (or something) and be united, but NOT mixed in the person of Christ
Sure He can, just as God used clay to make Adam. But in this case, the "clay" was human flesh related to david, Abraham and the first Adam and, in extremis, to all of us.
You are stuck on the visible. Christ is also human because He took on human nature, that is – he made Himself a human being without ceasing to be God.