Sorry for the long post! Basically ever since Mother's Day this year things with my MIL have gone downhill. She gets extremely jealous and is hyper sensitive about everything.
Last month my DH called her out for spending more time with our nephew than our 2 kids which she got upset about even though it was all true. After a blowup between DH and his alcoholic brother, that relationship is over, and MIL said really nasty things about my DH who was trying to help, and caused even more family drama.

At this point it is DH and his older brother vs. MIL and younger brother. When my BIL visited her house last week to see his visiting great aunt, she verbally assaulted him about how he never comes to see HER, doesn't bring the kids around, and physically grabbed my SIL blaming her for all their problems.

DH is 100% ready to cut ties and has; just like he did with his dad 2 years ago. I have been trying to keep peace with her for our kids sakes but its just so awkward I never know where we stand.
I have told her if she wants to see our kids that she can ask me anytime and in 3 weeks she hasn't asked once, but will send me sad emoji's saying that she misses them so much.

Biggest issue - we live next door.

I'm just not sure what to do at this point. I feel like I'd like the kids to have a relationship with their grandma and have it not be 'our' fault if they don't. Her attitude is she's done no wrong, she will not apologize to DH for her actions, and she will not talk to anyone unless we reach out to her first.
I msg'd her yesterday about watching DS for an hour and ah half and she never answered, and yet I feel bad because we didn't bring the kids up to trick or treat.

TL;DR: MIL has mental issues, do I/how do I cut ties?