what time do you close? if they are asking you to take the child after you close....no go! you will resent it after so long. if they are just asking you to take the child within your hours but a long day....consider charging extra to make up for the longer care provided.
I close at 5:35, if any picks up after that they owe me a 10$ late fee at pick-up.
I take a lot of nurses kids...they work 10 hour shifts...I don't mind as long as it falls with in my hours, anything after 9 hours though has an extra hourly charge. They are all ok with that.