'No mom, you cannot move in with me. You can move with [brother] who offered to help take care of you'

She needs help. That doesn't mean that *she* gets to dictate the conditions of this help.

Your brother offered to take care of her, so this is her option. She can take it or leave it. If this is an inconvenience to her, just too bad. Again, she is the one who needs help, so she is the one who will need to adjust and adapt, even if she doesn't want to.