It sounds like she's not physically ready to give up naps with those tantrums. But it's so frustrating when you know they "need" it, but they won't sleep! Have you tried moving her nap time back an hour? I found that helpful when my daughter started resisting naps (she's 3 1/2 now, and still takes one most days). I also use a white noise machine, because at that age, they're interested in every little noise they hear downstairs. I tell my daughter she doesn't have to sleep, but she does have to stay in her bed for "quiet time". She sometimes reads books, plays with her stuffed animals, etc. I use positive reinforcement (a treat or extra 1/2 show) for days when she actually sleeps. That seemed to help motivate her to go to sleep. I put m&m's in a big gumball machine where she could see them, but not reach. If she sleeps, she gets a small handful of m&m's when she wakes up. She does not like it when I say "you didn't nap, so no m&m's today"...so the next day usually goes better. If you can't find anything that works to get her to sleep, I'd agree with other moms....put her to bed early on every night that she doesn't nap. That way she won't be so tired the next day. I also tell my daughter that she can stay up later & have extra books at bedtime, on days she takes naps. It's working for us! My daughter goes to bed at 7:30 without nap, and 9pm with a nap.
Best wishes!