NTA - sounds like you might be taken advantage of, even if it is for a good cause since the kid is an innocent party in all this.

Doesn’t excuse the mother’s behavior though. Remind her that you tackle a majority of the responsibilities, and she would have to clean the place no matter where she lived.

If she believes the grass is greener on the other side, politely let her find out. Hindsight is almost always 20/20.