Do you have nap time in your contract? You need this time, I can't think of a care provider that doesn't.
Is this the moms only kiddo? Kids need naps, and lots of sleep too. Is the mom trying to get her kid to bed earlier for personal reasons? Regardless...not really your problem. Child naps at your place, required, or it will lead to behavior issues from being overtired in the afternoon. Mom needs to put on her big girl panties and enforce a bedtime.