I charge $5/half hour late fee after my closing time of 5pm. I would need a lot of advance notice to keep a child even 15 minutes late. No way would I let a child stay til 7pm. That's INSANE!

You should hand them a bill for overtime charges in the morning, including any charges for your appointment if you had to cancel it. My doctor charges $20 for a missed appointment, I think that's fair! Time to be tough a&b!