It sounds to me (and I could be wrong) that you asked DCM to pay you for a full time spot even though her Friday was going to be rotating.

In that case - the right thing to do would be to let her use the day because technically she has paid for it and it is her spot that you asked her to pay for.

I can totally understand why it would be terrible luck on your part though since you have an appointment already set up.

I agree with everyone who said that maybe this needs to be readdressed with the mom and put into writing very specifically on whether these alternate Fridays are hers to use or not.

Good luck - I hope it all works out tomorrow