I agree with what everyone's said regarding her behaviors and having her evaluated and stuff, but I wanted to say a few things regarding her naps:
-Both my kids were poop smearers. The one with the biggest problems right now only did it a few times, but the one without major problems did it pretty often. It's gross but I don't think it is that unusual... we ended up putting full length PJ's on him... backwards, so he couldn't undress himself as easily.
-Have you considered giving up nap time? I don't know if there is some norm that I broke by doing this, but I took my cue from my mom. She said I had stopped napping by the time I was two. I didn't want to nap, it took forever to get me to nap (if I even did), and then at bedtime, it took me forever to go to sleeep. So she stopped giving me naps and without that rest period, by the time it was the evening I was much easier to go down. And then, the same thing happened with BOTH of my kids. I know they expect it at daycare, but whenever I was in charge, I would let them stay up through the day and then had a consistent bed time, and it seemed to work well for them.
-Also, I know a lot of us have heard "sleep begets sleep", and for my family, I think it was true, but I know it isn't for all kids. Have you tried an earlier bedtime to see if maybe she would stay alseep longer? And, if that didn't work, have you tried a later bedtime?