I charge per day too. Any parent can stay beyond their normal pick up as long as it remains in business hour. Yes, it hard to schedule appointment and might be nice to knock off early if all gone but same for parent too. Not issue as long as here before close.

If I was finding too hard to do family errand/appointment, then I would shorten business hour but like last minute customer run into store, parent can pick up here last minute too.

Only time I expect early pick up is if I open earlier than business hours for them. If I agree to child come 30 mins early, then I expect my time back at end of day with pick up 30 mins early. Otherwise I assume working until close and bonus if they get here early.