Hi T.! Boy can I relate! Now my boys are teenagers and bigger than me now, but...
When my second one was 2, I gave up on naps for him. What had worked for the first one was not working with him. He was never a great napper anyway, sometimes 30 min- 1 hour was all he would go down for. When he was 2, it became this huge battle first to get him down for the nap, then again at bedtime. So I just stopped the fight, cut out the naps, and finally, for the first time in his life, he slept through the night! Now I'm not saying it was easy, cause I liked naptime myself. But, it was so worth it to get better rest at night. He would occassionally have an accidental nap here and there, in the car running errands, or if he played really hard at the park, he would come hme and just sort of melt. But overall, it worked out so well to just not have that planned naptime any more.
Now my older one has had a different issue. As he became schoolaged, then preteen and on up, he has had a lot of problems with falling asleep at night due to anxiety issues. He also has tremendous allergy problems and due to the combination of both, we had him tested for sleep apnea, which he tested positive for. The advice we were given by the doctor (a neurophysiologist) was to sleep deprive him. It really took me by surprise that he would suggest such a thing for a then 10 year old. I had always been a pretty firm believer in early bedtime for kids. But this dr. wanted us to keep our son up until 1 am, then wake him up at 7 am! It was rough, but my husband and I took turns with who got to make sure he stayed up late, then who go to get up in the morning with him. At first my son thought it was cool that he got to stay up so late, but within 3 nights, he was begging us to let him go to sleep. As much as we would have loved to, the instructions were to keep it up for 2 weeks. After 2 weeks, we could let him go to bed at 12:30, but continue to get him up at 7 am. Every 2 weeks we were allowed to add 30 min. to either end, but the doctor said for his sleep patterns, 11 pm was the earliest bedtime that we should expect, and to maintain getting him up consistantly at the same time. We have been amazed over the years how much better he has done with this regimine, sure was not what I would have expected. Now he is a senior, and will be going away to college, it worries me about how he will do with his sleeping. If he doesn't get good sleep, his behavior changes. Fortunately, it will be a school that is just a coule of hours away, so I feel like we can keep tabs on it.
So it sounds like maybe your daughter could benefit from some seriously controlled sleep deprivation, if you can handle it. Good luck! S.