OK, take everything you just said about your MIL, and add a severe drinking problem and unsafe activities with the kids, and you've got mine. Ditto on the husband with a mommy choke collar implanted making it impossible to say a word against her. I hope my son has one of those.
Actually, I feel like my husband's sweet, non confrontational (for better or worse even when you need him to be confrontational) personality is a coping mechanism he developed being raised by her and yes, he is truly used to it. She positively frightened me when I met her and in public, many people-waitresses, etc are startled by her abrasive rudeness, but her little family of followers and loyal husband appear not to notice it. I have heard comments about "oh you know her" chuckle chuckle amongst them, but they've all decided to support her and enable her. It blows my mind, because if I acted that way, I feel I wouldn't have a friend in the world-even my husband, but somehow it's OK for her.
In the early years of our marriage, I fought for his understanding of my side through really horrid episodes in which the kids were endangered by her, but got nowhere. I even tried the old fair is fair game. My family is crazy too in totally different ways, so I would indulge him when he would roll his eyes at my crazy mom and say, "I know, she's driven me crazy my whole life, but she's done such sand such good thing and they're only staying 3 days (the rule)" Hoping that when his mom came I could be like, "Since my family only stays 3 days and I admit they're crazy, fair is fair, yours should only stay 3 days, not 8 right, since last time they got so bored and ornery we all almost killed each other?" Blank stare. He doesn't get it.
Now, after 10 years, enough awful things have happened that I set the rules on their visits and ignore my husband's obvious annoyance at ME. I never try to make him see my side anymore, or make him handle it or talk to her about anything, even though he should. He won't. That's all there is to it. This is an issue with him that will not change. In his defense, once he did try to tell them to leave after they came at the last minute, stayed for 7 days, left for three, stopped back by unannounced and planned to stay another week, but when he told them we had plans and they had to be going she jumped down his throat and told him they could not change their plans. I had to step up and say we couldn't change ours either and we didnt' know they were coming so sorry, they had to go. She glared at him to shoot me down, but luckily he was scared of me too in that moment and didn't speak so she stormed off.
Anyway, some rules I had to set despite her huffing and puffing were, "No taking the kids away alone on long drives" when they visit. "No saying mean things about people" on TV etc, because my daughter was learning to insult people as second nature. And whatever else I have to say no to. I had to just tell myself the worst that could happen is that she doesn't like me. Otherwise I'm polite and let them do all the talking and white knuckle it through the visits and thankfully they live far away. I won the right to say no visits when my husband travels because they used to come wear me out while he was gone.
So, I hope your situation is not this bad, but it sounds similar. You have to set the no cursing rule. You have to enforce it. Even if it means saying to your kids, "Even though grandma says that, it's not OK, and you can't say it." in front of her. Be nice when you can so no one villainizes you, but hold your rules. If she beefs to you or your husband about it, ignore him the way he ignores you when you beef about her. I feel for you, it takes a thick skin. You may have to find a way to limit the visits if you can.
Ignore her when she yells at you or fight back. It doesn't matter. I've done both, it doesn't change the MIL in any way, so do what you want. Hang in there. It can challenge the marriage if you keep trying to get your husband to see the light. If you don't want to hate your hubby, just accept her as much as you can but hold your rules. If my husband sees me being nice to her, he has less of a tantrum when I enforce a rule to her. Stay calm. Good luck.