Both my kids didn't nap their regular naps at daycare, in fact my son only napped 20 minutes all day. Frankly though, I couldn't nap in that noise either. But when we drove home he fell asleep and they both needed to eat early as they were hungry and we ended up putting them to bed at 6:30! They normally go down at 7:45. Have you found with daycare they go to sleep early? My husband and I were surprised to have an extra hour to ourselves!
Re: Exhausted after daycare?
DD started daycare at 12 weeks - the first two weeks, she was so exhausted every day that she went to bed immediately after getting home.
She eventually adjusted to all the activity, and started taking (short) naps at daycare. We would get home by 6 and she would be in bed by 7.
She's transitioning to the toddler room right now, and the new room and playmates have her exhausted - half the week she falls asleep in the car and stays asleep as we take her out and just plop her into bed. We figure once she's fully transitioned, she'll adjust.
It got a lot better when he moved to the pre-toddler's room with scheduled nap.