I agree that issue #2 is the time she's dropped off. I'd would tell them (if nap time is at 12) that she has to be there by 11:30 and no later.

Then re: the crying.....give it a while for the new routine to set in and for her to get used to it. And at that point if she's still crying during naps.....leave her until she falls asleep/or nap time is over.