But since DD has yet to spend the night with H, is OW living there. Do I have a right to ask? Should I drive by just to see if her car is there? Do I have a right to check the place out if DD is going to be spending time there?
No. If your D was 5 then maybe, but for crying out loud, a 15 y.o. is going to give your H an absolute EARFUL if he does anything to anger her. One of my D's just turned 16 and if yours is anything like mine then she is more than capable of handling herself in that situation. Just step out of it. You've told H your expectations, but you can't force him to abide by them. D15 can though. If he screws up once he's going to have a heck of a time getting her to visit again.