Wow, I could have written your post. With a nap she was impossible - up until 10 pm and exhausted the next day, taking another nap, up until 10 pm, exhausted - repeat! UGH. Without a nap, she was in bed at 7:15 and got 12 solid, good hours. She would be slightly grumpy around 3:30pm, but a half hour later she would be fine.
Is the daycare flexible at all about naps? Right before DD turned 3, we asked them to stop giving her naps. They ignored me and continued. I asked again, and explained the situation again. Out of the 4 teachers, 3 of them complied with my wishes, and found out DD didn't turn into the devil
It was just better for her. Occasionally she still got a nap in daycare, I'd say once every two weeks, and we just dealt with the repercussions of that the next day.
FWIW DD is 3.5 and in pre-k now with no naps and gets her 12 hours a night and is fine. However, we still don't do 4pm driving! If we are somewhere, we try to either leave by 3, or stay until after dinner, and then drive home at 7ish, and if she sleeps at that point we can just transfer her from the car to bed. If we have to drive and she gets a nap, then we just stay in bed with her until she falls asleep (we do this anyway), and she flops and turns in bed and extra hour.