I probably would allow it partly because she is also keeping her home on the Wed so in effect using no days for the week when other families would likely send the child to care on the Wed and hope for the best so they aren't taking a whole week off work. I would allow the Friday but control the hours so she pays the regular rate but on Friday is the last to arrive and the first picked up or something like that.

Let her know that switching will not always be an option. Having said that I have always had a lenient policy that way if I have an opening but it is still my choice such as if I have two part timers which share a high chair then both can't come on the same day or we go to the park on a certain day and meet up with friends but have planned it for a day I have only kids that walk so don't need the stroller, etc.