Re: Nutcracker is coming!
I am in a unique position to help you, as I own my own ballet studio, and my wife and I are both photographers. We do all of our photography in-house.
Your idea is good, but do not try to do this at a performance. As a studio owner, I would never allow it. I would not want my dancers distracted. Your best bet would be at a dress rehearsal, or at the studio itself during one of the final run-throughs.
Yes, you should give them a percentage. You need them to promote you, and they are giving you unique access to their students. The studio has invested time and money in preparing the production and should be compensated. The minimum should be 10% of your gross after taxes, IMHO. Or you could offer a flat amount for each package sold.
Beofre we started doing this ourselves, I used to work my behind off to help my photographer. I even printed and prepared order forms for him with the pupil's name on them, as well as their character, to help him keep it all together. He sold more, and he was grateful. To my way of thinking, the better I made him look, the better I looked.
Hope this helps.