Hi D.`,
Making someone sleep is difficult. Routines change and patterns differ as they grow. You say no nap is out of the question because she's miserable w/o one. From what you describe, she sounds fine and dandy to me. I'm thinking it will pay off in the evening anyway when she finally konks out.
Don't forget the best time for a snooze is after lunch; any earlier and she'll be a wreck by evening; any later and she'll have trouble at night. Nap time at this age should be no more than ONE hr.
The explanation is simple, though the solution may not be: Two yr. olds fight the urge to rest simply because they're so interested in what's going on around them. Your curious child has so much to see and do and she's afraid that if she naps, she'll miss out on something. Avoid making naptime a battleground.
In the meantime, during her not so tired hours, why not try and read together, create a learning hour of spelling, numbers, etc. I know that would bore me to sleep, but kidding aside, make it productive.
I did like the movie method some gave; also, letting her 'crank' it out in bed, shutting the door is fine if you must. Even if a movie doesn't put her to sleep, she is distracted with something to hold her attention long enough for you to have your own time.
Remember that no nap generally means quiet nights. It's not the end of the world to not have one. As 2 yr. olds increase their independence, they often increase their fight against sleeping. Unless she really shows signs of being overly tired or crabby, it is not necessary that she take a nap.
Yes, at the 'terrible two' stage it dwindles down, and the hard fact of reality is... they need no nap at all. Sad but true. You'll get used to it Mom ;-))