I do agree that naps are important for children when they are 3 and under ( well technically I think they're important for everyone, adults included, but unfortunately that doesn't work! Lol) However, I do think some kids outgrow naps a lot quicker than others.

I have compromised and put in my contract that all children must nap/lay quietly for 30-60 minutes. If they are awake after 30 mins I will get them up and they can watch tv, do puzzles or read books in the upstairs living room with me. If they are sleeping after 30 minutes than I will wake them after an hour as they obviously need it IMO. I've only had one who did this and she almost always fell asleep. She was 3.5. A mom of a 2 year old tried this for a couple weeks but than her bedtime went back to normal and so did naps. Just a phase the child went through.

I don't know what I think about naps/bedtime ....I do think they sort of go hand in hand but I also know a few kids who nap late, 2-4/3-5pm and they still go to bed between 8-9. I don't think an early afternoon nap (1-3pm) should be affecting a child until 10pm but who knows?? Every child is different I guess.

You need to decide how important naptime is to you and decide how long you'd like nap to be and stand your ground with the parents. For me, an hour child free is good and honestly, the last hour with the child playing quietly has never stopped me from doing my cleaning, art prep, browsing online etc.