It's not that she "wants" to live with it ... as Sockpuppet said, MIL is afraid of retribution.
That's why the "Chuck and Diane" situation next-door to my parents went on as long as it did. We all knew they were beating each other (and the kids too
) up every night. Problem was, that the cops were called...but as long as Diane didn't press charges, nothing changed. Chuck would get put in the back of a squad car, dumped in the drunk tank, and would be home the next day. Lather, rinse, repeat.
Other than that, everyone was reluctant to call family services. They were afraid of Chuck...and what he might do. Chuck usually got violent when he was drunk. After seeing the damage inside that house--holes in walls, smashed furniture, doors kicked-in, etc. I can understand that.