A Daycare that doesn't allow diapers?? What do the kids wear during the day - regular underwear? Are they potty trained during the day and just having trouble at night?
Maybe you are dressing them too warmly and they are hot.
If they wear underwear during the day, maybe they just don't like the pull-ups. Try getting some of the thick training panties (they hold more) and also putting some vinyl training pants over that. That way, it will at least keep things a little drier. My son was 3 before he potty trained and my daughter 2 years 10 monthsa so they might still be a little young. My kids both trained very quickly once they were ready.
They both trained in 7-10 days. We just threw away the pull-ups and used regular underwear. We had to stay home for several days but it worked. Good luck.