I think he might be napping at daycare because he's used to it, not that he needs it, necessarily. I'd get daycare lady to stop the nap, since you're paying her to look after him. Is she preparing the room for everyone else to sleep and he's picking up on the cues?
Can you run through a week for me?
Monday - daycare, 15min nap @ 9:15; 1hr nap at home @ 12:30
etc.
I had DS napping shorter at daycare and longer at home, literally would never nap long at daycare, so we did a mix of 1 and 2 nap days for a long while.
Am I correct in thinking he's at daycare for a few hours in the morning? What are dropoff and pickup times?