Yes, they are pulling a 'fast one' on you. However, if you are taking their fees for the day..then technically you need to stay open for them. It is in their right to change their mind and bring their child to care since you are technically 'open'. It sucks and it is low handed I agree....but at the end of the day...they are in the right. You should not be charging for a day off (unless you have paid days off in your contract). In future, I would not be telling anyone about an appointment or other commitment on the off chance that no one arrives to daycare that day (or week) because of THEIR choosing if they are still paying.