My 3-year-old went through a period of not napping most days of the week (even though I was putting her down for them), and she too had Nwings and generally poor sleep those nights. I kept on and she's napping again.
FWIW, My 3-year-old's bedtime is between 8:45 and 9 pm on the days she naps (I push it up and hour if she doesn't nap). There's just no point in having her go to bed earlier because she will not go to sleep. She usually wakes somewhere between 7:15 and 8:00 on her own, though occasionally I must wake her. If you just made bedtime later and maybe changed up the routine (this I think helped us most with the bedtime battles-- they do tend to get bored with the same-old, same-old night after night and act up), maybe you'd have fewer battles? Also, my DD1 really needs a longer wind-down now than she did at 2. We now do bath, then books, then we tell stories in the dark in bed, then we turn on a CD of soothing music and if it looks like she needs it, I do a child-friendly massage game (tell her I'll turn her into a pizza, then need the dough, roll it out, spread the sauce, etc., all the while using gentle touch to calm her.) After two songs have played, it's time for us to go and she knows that. Lately the bedtime battles have stopped-- and they were TERRIBLE 4 or 5 months ago.
Anyway, just a few ideas.