I would think, that the legality is covered in the fact that your program is extra-curricular or in other words, an Elective. The participation of the student is voluntary, band is not a required subject needed to graduate, so on and so forth.

Math, English, Science, none of these requires that you purchase an instrument or mouthpiece, none of these need you to put out x amount of dollars each year to participate. And I'm sure that you probably already know this and have probably communicated this to the parent.

One of the things you need to consider is, are you willing to lose the kid, and that is what the parent is essentially threating you with, in order to keep the requirement of lessons for your top band. Not a lawyer, but I don't see how they can legally stop you from using this as a requirement. If your admin supports you, then they need to contact the parent and and support you!

Questioning the legality of this and actually doing something legally is (are?) two different things, and the vast majority of those that do the questioning will decline to even ask a lawyer for advice. My suggestion is to stick to your guns, unless some other variable comes into play.