R.,
Welcome to the world of parenting. ;-) Our now 5yr old stopped napping at 2yrs also. Same issues. He wasn't tired and toward 5pm he became a little devil. He quickly EARNED the nickname of "LITTLE MONSTER". (Satans' child) By about 5:30-6pm he was so tired that he would fall asleep for a couple of hours in his grandpas chair. This was awful because then he would be up late and sleep late. What my hubby and I figured out was that he was no longer a napper and that he needed tons; and I mean tons of sleep. (If he didn't have kindergarten this year, I would be a wreck.)
This is a super tough time and what we did was ask ourselves, "is he hungry or tired?" For him, he needed both. My husband would feed him, give him a bath or shower and read him a book in bed. This helped me tremendously because it gave me a "mommy time out" and I didn't have to feel like I was the only caretaker. (We have two boys)
Learning how to read your child can be difficult, but from your request, you have completely figured it out. You might also try feeding her more. Oatmeal or rice cereal helps kids fall asleep and keeps them asleep longer. Try this at night and put her to bed early. (6:30-7pm)Since she requires more sleep, going to bed early won't change the time she wakes.
A mom I know has 3 children. What she used to do at night was put them in the car and drive around for a little bit to get them to fall asleep. This might help you at nap time. What I did at that time was put on PBS (Ch 10 in our area), give our son snacks and I would nap in the same room. This year, our son is still a little challenge, but tons better. I give him lunch, he does homework or an activity book and sits down to play quietly. That gives me time to rest in the SAME room so I can function after our oldest gets home from school.
Being a mom is the most difficult job in the world. I have been in your shoes twice and thought that none of us would make it past 3yrs old. I had to look forward and see that other mothers went through the same thing and they survived. Growing out of naps creates an exhausted mom and a frustrated child from being tired. Try to help her with words to describe how she feels. This too will help with the battles. She knows something is wrong but doesn't know the words to describe how she feels. Help her. (Frustrated, hungry, tired, angry, etc.) This helped us too.
I wish you the best of luck and a future of peace and "mommy time outs".
Many blessings.