Non stop crying after very short nap

Hello, I have an 18 month old who started about 3 weeks ago and it's his first time away from home. He took a bit of time to adjust but he is good now except for naps. He cries himself to sleep which takes about a minute. Fine. No issues there. The issue is after the nap. He wakes up after 15 to 30 minutes and will constantly cry and calls out for his daddy. He also stands and walks in the playpen. I have tried sitting there until he falls asleep again. Sometimes this works and sometimes it doesn't. When it doesn't, I mean he will be laying down but crying constantly no matter how many times I talk to him about it. But at the time I thought, at least he is laying down so that's how he will fall asleep. He falls asleep again after an hour or more. I have also tried sleep training like letting him cry it out and go every 5, 10, 15 minutes to tell him to lay back down. But this doesn't work because he already took a nap for 15 min. He has his teddy bear and blanket from home for comfort but those don't work. I've tried taking them away from him if he keeps standing and he just hands them to me. I've tried letting him cry it out without going in to talk to him and that sometimes work but sometimes doesn't. Again, he may fall asleep again after an hour or more or sometimes he doesn't. As soon as nap time is done, it's as if nothing happened. I talk to him about how loud he is after nap time, and he laughs. I think he understands what I am saying but I'm not 100%.

Some background information: his dad used to rock him to sleep. And naps were always in a playpen in their living room where everyone is hanging out. Naps were always for 2 hours before starting daycare. Since about 2 weeks ago, they have sleep trained him. However, they are usually out and about on the weekends so he naps in his stroller or wherever he is.

I've never had a child that took this long to adjust to naps. Luckily I have 1 full timer who is a deep sleeper and as long as they are in a separate room, it doesn't affect him. My part timer is a light sleeper and can't nap with the crying. I don't want to give him books or take him out in case the other kids want to do the same thing. Plus I know he is tired and can fall asleep if he calms down. I also have a 3 month old of my own to take care of and nurse so sitting there the whole time is challenging for me.

Does anyone have any advice on how I can get him to lay down quietly at least?

I stopped using playpens and start using Kidco Sleep pods. They can't stand up in them. I find that they sleep much better and longer in them. It can take up to two weeks for the child to get use to them, but once they do, nap time is much better.

you can try rubbing the childs back and singing softly. I don't recommend rocking the child. When we have more then one child in care, its not practical. The child will learn to sleep at daycare without being rocked, it just might take a few months.