IMO, if she is paying you for the day than you need to be available to watch her children. If you are not available those days than she should not be paying you UNLESS you and her had discussed this and it's in the contract.

I'm assuming you have no other children on these Friday's? Does she know that or did she just assume you had other children and was paying for the day because she pays for the spot?

I have a similar thing with a parent here. Every other day her child is here until naptime. She pays for the full day though. There are times that she asks if he can stay until the end of the day if she has dr's appt's or takes a full day at work (she's a teacher and sometimes picks up sub shifts). She is paying for the full day so I don't feel that it's right for me to say no.