What's more important for your DH, that his kids have a strong relationship with his mother/parents (is there a FiL, as no mention has been made of him?), or that he has a strong relationship with you, his wife?
Your MiL sounds horrendous.
But so does your DH.
As is often the case, you have a huge DH problem here.
Your MiL hates you, bad mouths you, and tries to exclude you from extended family gatherings.
I would want nothing more to do with her, and I would be giving my DH an ultimatum - back me or we are done.
That's not you being coercive or controlling, that is you laying down your boundaries for how you are prepared to be treated.
Surely your DH can see that her behaviour is appalling?!
Why does he go to her after any argument and let her drag the details out of him? There's an easy solution to that one!
He probably needs therapy to understand the extent of her malignant control of him (and of his brother, and I expect the FIL too).
But however he does it, he needs to start standing up for you, and mean it. She will not change unless he does.
Good luck OP.