I also think your story sounds familiar, and unfortunately most of my advice is about the things we have tried that HAVEN"T worked. Of course, every kid is different, so some of these things might work for your daughter. I have two boys, 18 months and almost 3 1/2, who share a room and have since the youngest was about 6 months old. Bedtime ha s been 7:00 for years, although sometimes it ends up being closer to 8:00 by the time we get them into bed. Until recently, bedtime was not an issue: we put them in their room and left, and a short time later we heard no noises. However, for the past 1-2 months, the older one has been finding every excuse under the sun to talk to us, get out of bed, or disturb his little brother. The older one has a toddler bed (which he has been using for a while now), and the younger one is in a crib. The first thing we tried was telling our older son that once we tuck him in we are not coming back in the room unless he has gotten up to use his potty (we put one in his room so he couldn't say he needed to use the toilet in order to get out of bed) and needs help cleaning up. He hates having to tuck himself in, so if he gets out of bed and then can't get his "tuck," he does get upset -- but it didn't make a difference in his sleep patterns. He takes an extremely long nap (traditionally 1-4 or 5), so we thought perhaps he was getting too much sleep. We tried waking him up early from his nap, but he was just cranky in the afternoon and still didn't go to sleep any earlier. Then we tried skipping the nap altogether, but that had similar results. Next we moved naptime earlier in the hopes that he would naturally wake up sooner but still refreshed and then be able to go to bed earlier. Napping went fine, but nighttime sleeping did not improve. Last night we tried putting the boys to sleep in separate rooms. I will try it again tonight, but so far I am not sure whether we got any improvement other than not having to tell them to stop yelling at one another to go to sleep (which has been the latest antic; each boy says he can't sleep because the other one is making noise). The older one still didn't get to sleep until about 9:00. I think the younger one did fall asleep earlier than usual, but it took him a while -- probably because he was upset that his brother wasn't in the room and that he was sleeping in a different place (we put him in our bedroom, which is where he usually takes his naps).
So I haven't found the answer in our case.
However, I do one suggestion for what you might try with your daughter. I'm sure there are exceptions out there, but I really think 2 1/2 is too young for her not to be napping. Are you putting her down for a rest and she is not falling asleep? Or have you just given up putting her down at all? I have heard that overtired children can actually have more trouble going to sleep at night, which seems counterintuitive. I would definitely try to get your daughter on a nap routine. It's key that it's always the same time every day -- don't try to gauge whether she seems tired. Even if she isn't going to sleep, leave her in there for at least an hour for a rest. Eventually she will probably start napping (especially if she is already falling asleep in the car during the day -- this seems to indicate that the issue is not that she isn't tired). There was a period when my older son told me he didn't want to take a nap, and in fact he was not napping. He went from taking marathon 3-4 hour naps to taking no naps, just like that, and I was scared I'd lost my precious naptime with no warning. I kept putting him in the crib (he sleeps in a crib for naps because otherwise he gets up and plays) and telling him that he at least had to rest, and after almost 2 weeks of no naps, he suddenly resumed his old nap schedule.