I have it in my contract that full days fee is due if I close early for appointments. I let them know that I do my best to get the last appointment of the day so I can be available for the majority of the day versus closing for a half day on them. It has never been an issue.

I would still charge a full day fee in your case...though I would generally do my best not to have to close right in the middle of nap time (I assume you didn't pick this time slot). It's life you do need to take care of yourself and you can only do that by making the occasional appointment during daycare hours. It is a part of choosing home daycare.