Based on the title I'd say let the mom move in, she raised you. Help her out.
But reading the article tells me,do not let her move in. She moved in with brother and didn't watch the kids as the agreement stated. Plus created problems in the marriage.
Yeah I'd tell her if she needs help hit the welfare office.
Fun fact : in many states in the US if you let her move in, the welfare office won't help her on housing assistance because the welfare office will look at her income plus your income. Which means she has to much money coming in to get help, and now she can't move out.