My mom used to tell me that if I ever wanted to change my mind, their door was always open. Courts will, indeed, take a child's desire for where they want to live, into account after a certain age. It varies from state to state. I wound up a couple of weeks before my 16th birthday, living with my mom anyways under its set of circumstances. A written signed note was the only thing needed between my parents to get that ball rolling with their lawyers long before the official courthouse documents were created to change the custody and child support arrangements.
It's a nice gesture. Whether or not your daughter acts on it is a different story.