Your mom should contact the tenant's rights group in your area to find out what recourse she might have for the landlord not paying the mortgage. I'm sorry that the landlord let you/her down.
Even if she never gets child support (my mom didn't), your mom should focus on things like legal separation and getting his name off any and all accounts so he can't deplete funds. She should also start new accounts in her name only. She can see if legal aid in your area can help with any of it. Turn him into child support enforcement. My father worked under the table and didn't pay anything til he got a state job and they caught up with him. By then most of it went to our state to pay back benefits Mom had to use while he slacked off but...your mom has until the youngest child is 18 to settle up, so let it start to accrue and let them find him for her.
Is your brother in school? She could talk to the guidance office there and at the very least ask them to keep an eye on him and report any weird bruises. They are mandatory reporters and maybe if the school knows his home situation, they will not overlook changes in behavior like they might under different circumstances.
My mom struggled a lot to raise 2 kids on a teacher's salary. Tell her to be strong, find out her rights, and don't give up.
I also urge her to get the legal separation and divorce ASAP. My SIL put it off and when her estranged husband died, the bill collectors tried to saddle HER with HIS problems. It was a lot of heartache to get through it.