If you get 4 contractions in an hour, take the drug (with lots of water and then lie on your left side), and then if they continue at regular intervals go to LD. That's what I was always told, although if I had 3 at evenly-spaced intervals, I didn't wait for a 4th. Give the drug about an hour to work and then if it doesn't, go straight into the hospital (eating a PBJ first, of course...haha).
Also, sorry, my no-NICU comment was when I thought you were 35 wk. DS was born at 34 wk and still needed a 10-day NICU stay, even though he was 5lb 11 oz and wasn't on breathing support. My friend delivered a 4.5 lb baby at 35 wk in the same hospital and he was not taken to NICU. But then again there were 2 full-term babies brought into the NICU while DS was there so maybe I shouldn't have said anything.
Your DH is so right...they don't come with manuals! At least going through IF treatments and then pg, you have people telling you what to do all the time, but then once the baby's out, they're like "well, see ya!" DH and I felt that way when we brought DS home...because after 10 days in the NICU with all kinds of monitors beeping at us and nurses weighing him 2x per day, recording how much he pees and poops, we were totally like, "wait, how do we know if he's breathing??" "is he eating enough?" "why is it so quiet??" LOL. At least you have us on the bb to ask!