It’s not about what and how they see things. They cannot physically put anyone on a plane and move her to a different state.

That’s not legally enforceable.

Having said that, they also don’t have to buy her property. It’s likely that she agrees with going where they tell her to go because she is dependent on them. Controlling or not no one can make anyone do anything. She likely agrees to all this as they support her so it’s a mutual agreement