She probably could go to a shelter and ladder her way up from that to housing. But she won't do that, because she refuses to go to a shelter. She did once, but the shelter director saw Melinda doing something that concerned her enough to call CPS. From that, Melinda learned that shelter workers will call CPS if they see her neglecting or abusing her children. So now she flat out refuses to utilize that resource.
Melinda claims, of course, that the shelter director was just a Bad Goy discriminating against a righteous Israelite FOR NO REASON, but you can rest assured that isn't what happened. People that are trained in recognizing neglect and abuse generally do a good job in picking up on it when they see it. That goes double for shelter workers who see abusive and neglectful situations all the got-damn time. When the director called CPS, she had good reason to be concerned.