What could Trump do about it? It would be up to the courts, and both sides would have to argue the legality of the orders. It already happened with the “non Muslim ban Muslim ban” Trump tried to enact when he was president previously.
A “national divorce” would mean civil war, and nobody wants that. Even the people that want that don’t really want the reality of a war on US soil.
But the courts can't force the blue states to do anything either really. Just ignoring the orders would mean that trump would need to start hostilities to make them do anything. And if I understand things right, the military isn't allowed to get involved in a conflict inside the country. But maybe I am wrong there?
Traditionally it comes down to the national guard. During desegregation the national guard was deployed to several southern states to enforce the law when southern states tried to ignore it. They're not officially military so they don't run afoul of the posse comitatus act, but they effectively serve the same function within US borders.