If SHE cut the lesson short, then you shouldn't feel obliged to give her the full amount. If it was you that called it off, then IMO that's different. She should have at least offered to give you another half hour at another time, if she was demanding full payment. But if you've already paid, then I think it's too late to argue about it.
Regarding her teaching, it sounds like you'd definitely be better with someone else. You can always tell her the new instructor's a family friend or such, to avoid bad feelings.