I can appreciate that it might be difficult for OP to completely stop inviting BFF to paid events since everyone wants BFF there and they all have a good time. It's a little bit of the old "cut off your nose to spite your face". If OP and her DD didn't care whether BFF attended that would be one thing, but they do.
Maybe a good compromise would be, if DD is featured in the performance and really wants her Aunt there, Mom and Dad can invite Aunt and buy her ticket. However, when that's not the case, they don't. I would imagine there are times when DD has a small part or is part of an ensemble and it wouldn't be a big deal to her if only Mom and Dad were there to watch.
I would be upfront with BFF about the compromise so she knows where everyone's expectations are and there are no hurt feelings when she isn't invited to (and hosted for) every performance. Something like "I've been giving the school performance issue a lot of thought. On the one hand we agree that the price of a ticket isn't very expensive, but on the other, just as you feel you shouldn't have to purchase your tickets, we don't feel that we should have to purchase all of them, either. Lets do this- I'll still let you know about all of the free performances but from now on when DD has a ticketed performance we'll only invite you to the ones she's featured in, at our expense, and you can skip the ones she's not. As for the upcoming event, we're happy to get your ticket to join us on Friday but if you want to be there Saturday, too, you'll have to get your own."