Yeah it sounds like you set aside 22 hours per weekend for them, and they guarantee payment for 10 of those hours. So in my opinion, canceling on Saturday bring the hours you set aside for them down to 11, which she is choosing not to use by going away for the weekend. I think you should still get paid for 10 hours.
They were hedging their bets when they decided to guarantee less hours than they wanted reserved. They assumed that they would come out the winner most of the time by using more than 10 hours per weekend, but getting to shift them around as it suited them and never having to pay for all of the reserved hours. Well in this scenario, it bites them in the butt. You canceled one day, but still have more than the guaranteed amount of hours available to them, which they aren't going to use, but should still pay for according to your agreement.
I'd ask them what they plan to do, and if necessary present your reasoning, but going forward CLARIFY what the schedule is, what hours are to remain open for them, and whether they are guaranteeing a particular schedule (5 on Saturday and 5 on Sunday, or 10 for the weekend).