I know what you are going through. Our daughter turned 5 in September and has never slept well.
First of all, I would talk to the daycare or possibly find another one. Our daughter's last daycare would also require them to lay down for 2 hours, which was ridiculous for her. She hasn't needed more than 8 or 9 hours of sleep per day in years. We switched her into a preschool program (that is also daycare). They have studies in the morning and afternoon and only have a 1/2 hour quiet time. The teacher is very good about letting the kids stay awake as long as they are quiet during this time. I think the teacher is more aware of not needing a nap, too, because the class is specifically set up for 5-year olds who missed the kindergarten cutoff date (Mikah was 12 days after the date).
Secondly, I have found that bedtime rules have to be very consistent. We would put her down at 8:30 and sometimes she too would be awake until 11 p.m. However, she is not allowed to get out of bed, kick the walls, or make noise (except quiet singing or whispers). We tell her to lay still and be quiet or she will get a spanking (and she has on occasion). We have tried lots of tricks and some will work for a while, but then we have to change. For example, for a while, we had a t.v. in her room and she could watch a video. This worked for maybe 6 months. Then she started using the video to help keep herself awake, so we stopped that. We have also tried music. She has a computer in her room and we will put a CD in the drive and let her watch the flowing patterns of the Windows Media Player. Then I would start making her lay still and quietly for a while before I would give her the music (20 minutes or so). Sometimes we just have to keep after her, and she doesn't get anything. She has gotten better and she can now usually fall asleep by 10 p.m. We don't fret if she's not in bed at exactly 8:30, but we always shoot for around that time.
The other thing we have tried with her is different herbal remedies. Some people have luck getting their kids to go to sleep with Melatonin. It wasn't very helpful for us, but it was worth a try. Some people give their kids Benedryl, although then you may have a hard time breaking the habit. There was also a supplement recommended to me at the general nutrition store, but I don't remember what it was right now. For us, the best thing is for her to lay still. If she wiggles, she will keep herself awake.
You can try talking to the doctor, but ours never had many suggestions. Good luck! I know it is very difficult - the lack of sleep of one reason we waited five years for another child.
C.