I'm just going to give my two cents of experience with this situation since this dad and I are both from Texas and I have actually had a similiar situation in the court room.
We were told by the judge that both parents are allowed to pick ONE activity each to enroll our daughter in. We are both responsible for making sure she gets to that activity during our parenting time. However, we were also told to use 'common sense' in picking these activities. No competition or select type sports that would require hours of practice per week and all year long training. My daughter has been in dance since she was two. I know she is not going to hit it big and go off to New York to study in ballet (well maybe she will) but not before she is of legal age to do so (meaning 18). Academics always come first and she can't miss any school because of whatever 'sport'. This came up because our daughter wanted to try soccer and her father refused to allow her because he didn't want to spend 'his' time taking her to soccer games on Saturday's. Well it's only for a couple of months a year. It's not all year long. She also wanted to do swim lessons which I felt was very important too however, during the summer, the majority of her time is spent with her dad and he refused to take her to swim lessons. I had to get the court to order him to take her to swim lessons for two weeks. He opted to just not get her. (we live 20 minutes from each other and the lessons were even closer to him than to me).
If the kiddo wants to do this, then let her give it a try. If it effects your time so much that you are having to run from one end of the city to another on every day that you have her, then yes I see a problem that needs to be addressed. But if you are never effected because everything happens on mom's time, then what's the problem? My daughter also is in piano lessons but it's one day a week and will never interfere with her father's time. She also does choir and running club at school which never interferes with either of our time because it's at school. So it's fair to say my daughter is in multiple activities but as long as her father isn't being effected by the schedule then he doesn't care.
I can understand your concern about pictures and having them fall in the wrong hands, I think all parents 'might' feel this way at times with the Internet and so many ways for sick people to be around our kids but honestly, I think there is more of a chance of some sicko watching your daughter play with her friends at the park than in a photo shoot...
As long as it doesn't effect your parenting time, in my experience, it won't matter to the judge. And in our case, the parent screaming that they don't want their kid to do what the kid 'wants' as far as extra curriculars goes, is the one that gets slapped down. My daughter was disappointed that she could not audition for the competition dance team but that was specifically off limits because of the commitment that it involves and honestly, I don't believe it would be fair for me to tell her dad what he is going to he doing every Saturday he has our daughter nor do I want him dictating what I will be doing.