At 2 years old.... sleep tweaks commonly happens.
At this age, it is a real change in development/cognition and emotions. Emotions, not being fully developed yet, in a child this age.
Sure and they still get "separation anxiety" too, which does occur at different ages and is manifested differently per age juncture.
It is a lot of changes, in a kid this age. Developmentally.
Even if they don't sleep/nap, they do need it.
But at this age, they can 'fight' tiredness, better.
Or when over-tired, they get more seemingly "hyper." but are actually tired.
Try telling her, that it is nap time for MOMMY, too.
That is what I do with my kids. It is nap, for me too. And I do, sometimes nap. Really.
Also at this age, they don't have fully developed "impulse-control" either.
Or, instead of leaving her in her room and not being able to wind-herself down at-will... try sitting in a chair in her room. Tell her to lie down. You sit in a chair. Don't engage with her, don't give her eye contact, don't play, don't get into a dialogue etc. Keep it quiet and door closed. Turn on white noise if you need to. Make the room dark. Tell her it is wind-down time. Use that as a cue word. Tell her to lie down, to calm her body. Let her body relax. Meanwhile, you SIT in the chair in her room. Me, I do that and read my magazines. Every so often, in a monotonous boring voice, I will say to him "nap..... " with no emotion.
That is what I do with my little 4 year old Dude. That is what works. He still naps, everyday. He needs it otherwise he turns into a fussy mega Troll.
Also, if my son has to poop, he cannot nap. So, after any snack or lunch, after he poops, he is more able to nap. I know that about him.
Also key: is to have a wind-down time. ie: a transition BEFORE the actual nap time. Key things down, like 1 hour before nap. Kids this age, need that. To KEY DOWN.
Also, in the mornings, that is when I do physical exerting stuff with my son... outside. Lots of running around etc. To get his yah-yah's out and pent up energy. So that, by afternoon/lunch time, he got it out of his system, and will be tired.
Kids this age, still need to nap.
Have the SAME routine, every darn day, per naps. After a bit, the child will KNOW it, like autopilot. My son does. Sometimes even when he is tired, he will tell me "I wanna nap now Mommy... " and goes into the routine himself.
I teach my kids, that 'naps' are not 'bad.' It is good for the body and that it is okay to ADMIT that you are tired. It is healthy. Nothing is wrong, with being or saying, you are tired.
Also at this age, due to changing cognition and imagination development... kids do get night-mares and dream. Sometimes, this will tweak them too, and/or wake them.
Also what you might try, is teaching your child "deep breathing." This is a real technique. Tell her to lie down, make things calm. Then to deeply breathe in... and to slowly breathe out. Tell her to close her eyes when doing it. And to just listen/focus on her breathing... and not think of anything. It can be calming. For some people, it even helps with stress. Do it for as long as she can, rationally for a 2 year old.
For some, it will allow them to switch gears. To relax.
Last but not least: there is something called "Hyland's Calms Forte- for kids." Its Homeopathic, non-drowsy, all natural. Helps to calm a kid or adult. Some use it when traveling. As I have and my friends have. Found at Whole Foods or natural food stores. Look it up online for the reviews.
all the best,
Susan