I would stick it out or refund her 2 days. Terminating her without notice 2 days prior to her end date anyway and then not refunding her those days is really a terrible thing to do. Yes it sucks to have to spend the next couple days dealing with a problem child but unless you are prepared to part with the money (and sacrafice your repuatation a bit as I'm sure that the mom will be more than happy to tell people what a horrible position you put her in) suck it up and deal for 2 more days.

I know you are forced to put them in the same room but if he's not napping at all anyway what purpose is it serving to have him in a room where he disrupts others? Perhaps a playpen in the room where you spend naptime would be less disruptive. It gaurentees you won't get your break but it sounds like you won't anyway so you might as well perserve the sleep for the other children.