MIL- now upset at me for grey rocking and creating distance [update]

My last 2 posts here got quite a bit of traction so I wanted to post an update: https://www.reddit.com/r/inlaws/comments/1ql47ze/mil_was_impossible_during_my_wedding_venue/

There's the last one, the 1st post is linked in there.

Happy parts of the update: my wedding went amazingly. We did the courthouse and a small lunch and MIL was not invited. My BIL actually texted her to leave us alone and give us space during that week, and she never found out about the lunch. My husband and I kept a distance from MIL during the destination wedding trip, MIL was busy with her family and we were so busy with friends and my family.

There was only 1 incident- when we were about to walk down the aisle, MIL realized her parents were not in the lineup of people to walk down, but my husband's other grandparents were. Her parents are not close to my husband and I- they are abrasive drinkers. We see them 1-2x a year when they visit MIL. The other grandparents we see often. She told my husband "oh wow, seriously?" and started to get mad and he snapped at her and said "you are NOT going to bring this up right now" and thankfully she shushed. I only learned about this after the wedding, so thankfully I was shielded from this day-of.

Ever since the wedding in March, I have just been grey rocking and creating distance. I do not respond in the family group chat. I have seen MIL at family events and I am polite and say hi/bye but I do not interact beyond that or ask her any questions. She gave me a gift for my birthday in July and I texted her thank you and I can't wait to use what she got me, that was probably my first time texting her since March. To me a gift does not excuse bad behavior nor is it an olive branch in my eyes, but I was polite.

My SIL and I are incredibly close and she confided in me that MIL has been acting very negative lately, and she always tries to talk about me with them (BIL/SIL). She is asking them if they have heard from me lately, what is my deal with being so quiet, when do I plan on having kids, why do I have such a bad attitude (lol)... my SIL says she just shuts down the convo and says "you should talk to them, we have no idea" which I appreciate. SIL and I have an agreement that we will not discuss each other with MIL.

A couple of weeks ago, MIL's old dog passes away. I spent that day hosting SIL and nephew while BIL and husband went over to MIL's to comfort her. We were busy all day chasing down a crazy toddler and having dinner ready for when the guys got back to the house. It did not occur to me to reach out to my MIL that day, or in the following days. I was not intending to be malicious, I just genuinely have not been reaching out to her and was holding true to that boundary.

About 2 days later, I notice that I have been removed from our family group chat. My husband asked MIL why she removed me. She said it was unacceptable and "mean" that I did not reach out about the dog passing. She also said she has been "thinking about my bad attitude for a very long time" and that she can't believe how rude I was on my wedding trip. She said that she wants to sit down and talk with me and my husband.

I told my husband no. I said he needs to set his mom straight and tell him how rude SHE was acting on my wedding scouting trip, among the laundry list of other stuff she's done. I don't think its my job to sit down with MIL and try and convince her that I don't have a bad attitude, when I know it is not true. Historically, having sit-downs with her is not helpful because she has big emotional (crying, raising voice) reactions or acts like she has no idea what we are talking about when we cite her bad behaviors.

I told my husband he should be the one to straighten her out, and set a firm boundary that its unacceptable to a) remove me from the chat like a child, b) ask other family members about me and c) talk about my "attitude". If she feels unhappy with something I do/say, there needs to be an expectation that she talks to me in the moment like an actual adult instead of letting things fester or blowing up on me and then expecting me to want to be nice to her.

How would you handle this situation? Creating distance with her has genuinely brought a lot of peace to my life, but in this case it seems to have backfired. With a crazy MIL we are damned if we do, damned if we don't.