How to keep a kid awake during quiet time?

The 4 year old I nanny has a 45 minute quiet time in the afternoon after preschool (about 1:00). She inevitably falls asleep. If I let her sleep she doesn’t go to sleep easily for her parents. If I wake her up, she is miserable and sobs and screams for her mom. If I don’t keep an eye on her, she will just go back to sleep. I think her parents just end quiet time if she falls asleep and let her come down and play, but I rely on the quiet time to get some of my homework done. I usually just plop her down in her sister’s room to play with her toys, is she has fallen asleep, but I know her sister doesn’t love that.

Help me, nanny posse!