WHOA! You stopped me cold at the statement, "If our children want to be in the recital then they have to sit for pictures."
Ballet mom of many years here and I'm plenty mad on your behalf.
Don't let the fee and the photographer's income blind you to the real issue: Why on Earth deny a child a place she earned in a recital because she didn't have some photos made? This studio does not care about the kids' dancing, but it cares about these photos this much? Find a studio that puts dancing first. The junk about the program? Easily fixed,they just put a line in the caption saying, "Not pictured: Sally Smith, a first grader at.... who has danced for X years..." They are more focused on their program than on the show itself and yeah, it steams me.
The photos have nothing to do with your child's hard work learning dances and practicing and turning up for her classes. Nothing. I agree with the person who posted that it gives a strong whiff of the dance studio and the photographer being in cahoots on this photo package and the studio getting cut of this huge sitting fee. There is no, repeat, no reason the studio should REQUIRE a child to have photos made as a condition of participation in a recital intended to demonstrate the child's dance achievements. Basically they're saying that your child's year of work -- and your year of paying tuition, hauling your kid there to dance, etc. -- do not count, but a lousy set of expensive photos does.
Have you asked point blank: "What happens if I say my child is not going to participate in photos? Are you actually intending to stand there on recital day and tell my child, 'You cannot perform'?" Do it. See what the studio director says. I bet no one has ever put the director or owner on the spot like that. They are using the threat of "no photos, no recital" to force people to spend money. They are probably going to be scared if you bring it up because they fear if one parent rebels, more will.
Does the studio itself display the photos taken in these sessions? Here's why I ask: My daughter's studio has up years and years worth of great photos from shoots done before their Nutcracker and spring shows--professional shoots, done at the dance school. But the studio says quite clearly that NO one is required to be in these photos, and the studio would never dream of making performance dependent on photos.
And our studio uses photos in its programs as well, but doesn't try to have every child shown and named in every program.
If you dance school's owner says, "Well, we need the photos to put up here" (if they do that) I would just respond that it's not your business to pay for their studio's decoration. Geez.
And the $100 sitting fee, even if you weren't being blackmailed into paying it, is excessive. Our students do not pay a sitting fee at all. We pay a flat fee for each set of photos we want -- kids have multiple parts in some ballets/recitals but we can choose if we want individual photos of our child in just one part, two, three, whatever. We can get individual shots done and we just send in our order with our kid on picture day. We also can buy copies of the group shots, which are the ones the studio uses on its walls. But we're not required to buy a single thing. And a kid whose parents do not purchase any photos? Those kids are still very welcome to turn up and be in the group shots, since those shots go on the studio walls as a record for years to come.
What you describe is simply blackmail. Call them on it. Don't bring up how much the photographer is making. But tell the dance school owner that you question what the relationship is between the photos and the printed program, and the dance studio's ability to teach and desire to show its' students' efforts in a recital.