I ran FDC for a little while and whilst the example I am going to give you is an extreme boy with a few issues (whereas your little man sounds like a normal 3 year old), the behaviours were the same (not wanting to go, but having fun while there etc)

I took on a 3 1/2 year old boy and his sister who was 2 1/2.

The first month was great until the day came that he had spent the weekend with his grandparents, Monday came along and because he hadn't seen his mum (dad picked him up from Grans and brought him straight to FDC). He screamed the second his father pulled into my street - in fact I could hear him screaming half way up the street while still inside the car.

Dad and son came in, little sister had already settled and found the toys that she was happy to play with - but he just screamed that he didn't want to stay.

I asked Dad to stay for as long as he needed to - 10 minutes later both kids were "settled in".......Dad goes to say goodbye to the kids and son screams to go with him.....this is where I saw red - Dad lets him go with him and keeps the daughter with me.

From that day on, it became a daily battle for him to stay with me in care to the point that he would play until an activity was started that he was less than happy with and would continually scream "mummy, mummy, mummy" until I called his mother.

Now like I said, in this example he had some extreme emotional issues that were compounded by his parents own issues (so this part won't apply to you) however allowing him to call the shots on whether or not he stays created a MAJOR issue moving forward.

FWIW I'm not suggesting you force your son into a situation that he doesn't want to be in - all I am suggesting is before removing him from Care, keep doing what you're doing and talk to the carers, watch from the distance and when you can clearly see he's having fun, when he says at home that he doesn't want to go, gently ask why? It may be just a preference of being with mummy (which is totally understandable) it could be that he doesn't like something there that he hasn't yet told you or it could be that he is just saying that.

As for the hour and a half in the morning of screaming - I can absolutely understand why that would wear thin and be enough to keep him home. To that, I'd suggest trying to calm him down and try asking him what's wrong. See if there is a special toy he'd like to take to show the other kids or ask if he'd like to help you pack his bag with snacks he chooses etc.

Good luck with it all