"Mom, that sort of thing is court-ordered."
Tell her that she will need to go back to court to have the divorce settlement modified. You will be happy to comply with any court order, of course.
The money in question is child support. It reflects that the cost of living with a child is higher than living alone. Obviously, if you move out, that has a big effect on the child support claim!
Otherwise, you could have a big mess: Mom demanding the child support from your father, Mom also demanding it from you, and Dad demanding it from you to boot! That's why families don't resolve such things themsevles, it's done in court to assure fairness.
So Mom needs to go back to her divorce lawyer and ask for a modification of her child support so she collects it from you instead of him. The legal process will notify all parties, and each will be given an opportunity to argue their case.
Hint: No judge on earth is going to require a child to pay child support for his own self after he's moved out. That simply will not happen. But telling her that is obviously a waste of breath. She needs to hear it from the judge.
But you have given her a roadmap to get there.
Giving people money is no kindness
Wish people well all you like, but you do them no favors by giving them money, you simply become an enabler to their unwillingness to confront their own situation. Mom's plan for her financial piccadillo is "kick the can down the road", keep things the same one more month and solve those problems later. Of course, later will never come because it doesn't have to come.
Jesus said "Give a man a fish and he will not be hungry for a day." Jesus was too polite to mention that tomorrow you'll have a hungry man demanding another fish!