Most providers have a one hour rule - basically it is a time for each child to have to not deal with anything. Those that need to fall asleep and stay asleep as long as they need. Other kids rest the hour and recharge and then get up and do quiet activities - generally they are a year older than this child though.

It is possible it works at home because child is sleeping in a bit longer in the morning negating the powernap he was having before. Also they may be playing one on one with him to keep him going which is not something you intend to do at daycare. I would put him down as early as you can and leave him there for 45-60 minutes and then get him up if he is still awake but chances are he will be asleep .Try to wake him earlier than normal so there is a longer period between nap and bedtime. We do outside play after nap so they burn off accumulated energy and make up for the nap. I would be noncommittal but say child still needs to lay down in one place and rest while you clean up from lunch and eat yourself and then you will be able to supervise and give him attention. Do not tell mom if he falls asleep. Chances are even with a short nap at your house bedtime will still go ok.