Nap/quiet time is an absolute necessity for us! And for the kids as well. I would continue as you are, and if she is that angry about it, she can go before the month is up. Your policies are your policies no matter what. My theory is if the child falls asleep during quiet time the need the sleep.

I won't get much of a break come summer, as my son will be home and has special needs, but he still understands quiet time. He will play quietly on his own while I clean up and have a rest, and then we have some one on one time while the others are still napping.