Can you come to a compromise of cutting nap time shorter, but she still has a sleep?
For us, under 3 has a nap. No other options. 3 and up, will lay down quietly and take a break. If they are tired, they will fall asleep then. If not, then at least thier little body has had a rest, and a chance to rejuvenate.
I understand mom's desire not to have her sleep for 3 hours. I have a daughter that will do that and stay awake far too late. More often than not, I will wake her from an afternoon rest. But I know that she still needs the rest, just perhaps not as long.