Is it permissible for my aunt to change the people my mother designated to receive the sadaqah and give it to other people?

Your aunt is not permitted to violate the instructions your mother gave her regarding the method of distributing the money. If she violates the agency, she becomes liable. If the money was zakat (definition) and it reached those who are not entitled to it, then your mother's obligation is not discharged, and she must pay the zakat again. She has the right to demand from her aunt the money that was mishandled.