The way you have appointments and private lessons set is quite complicated. Here's whats needed:
We need to be able to see the room reservation options WITH the class calendar (not just bookings) so if I have a teacher who is doing private lessons in Studio A on a monday at 3-4, it shows on the calendar so when other teachers are reserving space, they can see that space isn't available. Yes, teachers want specific rooms especially if they're teaching right after. Also, a teacher may have private lessons on a monday in studio A but will have private lessons on Tuesday in Studio B. It isn't always the same studio and when you have 5 studios and 15 teachers, that's way too much to manage. We need a system that shows when a studio is reserved even before it's booked.
We need to be able to allow the parent to pay for the reservation but for us to still see the booking BEFORE it's reserved. This way, parents can pay for the reservation and not the teacher. AND, if you have your system set up to not allow purchases with a negative balance, prevents dancers with balances, signing up for private lessons.
I feel like the system that's here is close but makes no sense and doesn't give the teacher or the studio any control as to when people book or where other than giving their times and studio preferences.