Does my niece have the right to choose where she lives?

This is a heart breaking situation- your niece is essentially being abandoned. Unless a court has appointed a guardian for your niece, her mother's "designation" of a guardian has no legal effect. Your niece can sue her mother for child support, to which she should be entitled until age 21, as well as petition the court for emancipation. If the father is in the picture and paying child support to the mother, your niece can ask the court to order her mother to pay it directly to her. In the alternative, you or another relative can petition for guardianship. Although courts do not usually order child support be paid to guardians, given the circumstances, you may win if you ask the court to order the mother to pay child support for her daughter. It does not sound like your niece is ready to be emancipated. I hope she has a responsible, caring adult in her life who will petition the court to be her guardian. If you can obtain the mother's consent to the arrangement, even better. Good luck.