Oh boy, you were told not to let her nap? <insert eye roll here> because she slept in? Sheesh! Sounds like Mom/Dad needed a break this morning too. And so do you. My rules are, everyone naps. If they are not sleeping in their nap area, then they are quietly reading a book etc. I have to laugh...I have had 2 older (3 year olds) start with me where parents said "Oh, they don't nap"....in both cases they were so zonked by nap time they did nap, every single time.
When you say "time outs don't mean anything to her", with my own 3 year old was the same until I actually restrained him in time out (booster chair where they eat meals, with tray clipped on to restrain with timer on)...that worked immediately. You definitely need to find an effective consequence for these negative behaviors; have you discussed any of this with parents, what strategies work at home? Poor you! I have been fortunate not to have to deal with the attitudes/defiance, good luck to you!