Just ask the Mom if you want her daughter to have naps when she is in your care. Tell her you've been noticing how tired she is and ask her want she wants you to do. At 4 years old though I'm assuming she'll be going to school in september? Maybe the mom wants to wean her off naps. It's a process for sure though. If she naps at your place, then she stays up late at night and then she's tired when she gets to you and then she naps...it's a vicious cycle lol I would suggest stopping the naps, she'll be exhausted by the end of the night, she'll go to bed early and be refreshed in the morning. It'll take some time to get used to the new schedule for everyone involved. I would tell the mom that you will be starting "body breaks". That gives the child time to look at books, snuggle with a stuffy/blanket. If the little girl happens to fall asleep then I would suggest waking her up after the 30 min.