45, a hormonally unstable woman does not need to hear that her husband is an asshole. He has probably cheated on her many times, and it can wait until her body is in a more normalized state.
No, what's disrespectful is him asking the labor and delivery nurse out while his WIFE is having is kid. She should call him out on it right away, tell him to get his priorities straight.
She really can't do anything about it. If she were to try and tell the wife, call him out on it, or get involved at all, then the husband or wife might file a complaint against her. OP could get written up over that, or at least bitched out by her boss, for getting involved in patient affairs or behaving unprofessionally. It's horrible, but there's really not much she could do, except maybe send an anonymous note on her own time, but that's still really shady.
"hmmm. My wife is giving birth to my child. I'm bored. That nurse is kinda hot. Let me see is I make her think I'm a total dick." Yeah. Definitely not funny.
Wow what an ass hole. You should tell his wife. She deserves to punish him by making him watch the baby by himself for a month. Won't have time for flirting then! Hahahahhh.
I don't know if OP should say something to his wife... I mean, she's not related to them and she could get in trouble for not being professional (aka, just keep her mouth shut) about it. Also, I think that letting a fail of a husband watch your newborn baby by himself for a month, is actually a punishment for the wife. Unless his only job is being the diaper-changer and vomit-cleaner.
As others have stated, there's not much OP could have done. She'll probably never even see them again, unless she has to deliver their (possible) second child. Then if he does it again, she should do something.