It is absolutely normal to take lessons with as many instructors as YOU want, but it has to be your decision. I would be extremely upset as you are. If it is not the only studio where you live, I would ask for my money back and start searching for other alternatives, perhaps, independent instructor of YOUR choice. It could be wording in your lesson package that they can switch instructors, though. Check that first. If the studio owner is a true professional, I hope he would not hold you to that , and will return the money. It is not a good atmosphere. You are paying for private lessons. It has to be your choice. I used to pay for package in NYC large studio, but I only wanted to dance with one specific instructor. Only once, when my teacher could not make it, I was offered a lesson with another instructor for half price. (My teacher could not make it that day, and I already was on my way to the studio).