Is it just perhaps that she is transitioning out of needing a nap, she is tired but not enough to fall asleep? My older daughter stops napping regularly before she turned three and nap time became really rough because she was tired, but not enough to sleep. Then if she finally did nap, she would have trouble falling asleep at night. So her behaviour was not always so pleasant because she was tired and moody (though she wouldn't sleep, which was frustrating). Your dcg may have only been giving trouble at nap time at home first because it isn't usually as busy a day at home.

I am currently using a reward chart for my almost 4 year old, though I don't use food. He earns stickers, then after 10 stickers he gets a rewards that is a fun activity for everybody. The only was food rewards would be fair is if you gave them to all the kids every time, which I wouldn't want to be doing on a regular basis. His behaviour has mostly to do with how he behaves with his mom at drop off and pick up, I couldn't take watching it anymore so I suggested a reward chart. Happily mom was fine with it, she was really struggling. I has been working well for us here.