Awkward MIL situation

So, I’m 32 weeks pregnant. I didn’t meet my fiancé’s mother until after I was already pregnant because he never had a close relationship with either of his parents. He hasn’t seen or talked to his dad in almost 10 years and his mother got involved with an abusive alcoholic boyfriend who would beat her and manipulate her. My fiancé and his brother would constantly be running over to her house to try and protect her from her boyfriend after they’d get frantic calls/texts from her, the boyfriend even put her in the hospital from beating her so bad. My fiancé made it clear to her that he doesn’t want her seeing this abusive crazy boyfriend anymore and she keeps claiming she won’t - then she does stuff like text my fiancé a picture with an engagement ring on her finger 😒 from the boyfriend (knowing it would annoy my fiancé). And she will tell my fiancé it’s over between them but my fiancé will drive by her house and the boyfriends car will be in the driveway. ANYWAY - of course I feel bad for her, but ever since I’ve gotten pregnant she has told me she insists on babysitting my baby whenever possible because we live so close to her, or if either of us are at work to just drop the baby at her house. It makes me super uncomfortable thinking about leaving my baby alone with her if she keeps lying about being with that crazy abusive boyfriend and is clearly mentally unstable. Shes a really kind woman and I like her, but I can’t help but think she’ll have the abusive boyfriend over while she’s babysitting my child and I don’t want my baby exposed to that! Or my baby will be neglected while they’re fighting. And god forbid the crazy boyfriend tries to hurt my baby as well! The worst part is I feel bad even bringing it up to my fiancé because he loves his mom so much. I feel so bad that his mother is being abused and manipulated and I feel like a bitch if I refuse to let her babysit her grandchild on top of it, like she’s being punished for it. Not sure how to handle this one.