doctor boyfriend making himself scarce while I'm going through health scare would have been enough for me
For me too, but then I reassessed what happened at the end of 'Recession Proof' (where Cuddy really didn't look happy) and Cuddy's dreams during 'Bombshells'. She was right about the vicodin, which means that the dreams echoed her fears, and not her hopes. And a central fear is clearly that House's addiction would rub off on Rachel. In the first dream, where Cuddy is still around, she refuses House's offer of 'candy', but in the sitcom parody where Cuddy is dead, I think she accepts it. Either way, the thought of Rachel growing up with a relapsed House is a prime worry in those dreams.

they make a good bargaining chip for something I think he had decided to do anyway.
Quite. Nolan is right about Cuddy's offer of a scrip; it's absolutely counterproductive. It works only because it shows Pete just how desperate she is, and her desperation tips the scales in favour of what Pete rationally knows needs to happen.

Also Pete watching Cuddy's ass disappear, because one thing about House, he was always shallow that way :)
There's that, but I think he's also watching her disappear with a feeling of trepidation to which he doesn't want to admit, so when he catches Nolan observing him, he hides behind his lechery.

Thanks for reading and reviewing so faithfully.