I went through this last year... I had a parent drop her son off as soon as my door opened in the morning. She was able to pick him up at 2pm, but left him there as late as possible - many times she came well beyond the pick up time. I charged her for the times he was there past my closing time. I've heard every excuse in the book, including running out of gas.. the day after she told me how much it cost her that afternoon to fill up her tank.
What I did is I have different rates for # of hours. I have a 1/2 day 0-4 hour, 4-8 hour and 8-10 hour rates. The rates aren't that much more, but for a child that is in my care for only 5 hours shouldn't have to pay the same as a child in my care for 10 hours. I open at 7am and stay open until 5pm - however some days I have a child that needs dropping off at 6:30am (but are picked up by 2pm) and other days some children are here until 5:30.