It is really hard to ask your instructors to NOT work somewhere else unless they are getting benefits or at least enough hours to make a substantial amount of money. Personal trainers often work at several gyms in order to make a living, teachers in other forms of dance also often work at several studios, this isn’t very different.
She is probably a little nervous because of recession and competition, but many of the new studios popping up are just people trying to make a quick buck. There is a studio that just opened in philly like that and guess what? They are failing because they don’t really know what they are doing.
The owner has right to be concerned about her working somewhere else, but a simple discussion could put any of her fears aside.
Although not a studio owner, I had to sign a contract that said although allowed to work other places I will not discuss the business of the dance studio, will not use any of their forms, and will not cross promote myself. Also my contract is a non-competition contract that says if I am fired or leave that I cannot start my own pole business within 100miles for a year. All of these things are fair considering, pole dancing is a niche market.