I have been where your MIL has been, married 25 years before FIL left for someone else.
They are still together after 6 years and I have not spoken to him for several years.
It took at least 4 years for the anger and betrayal to fade to a point where his name could be.mentioned, and my then early teen children do an excellent job of keeping in touch with him separately. We have a rule that there are two separate lives going on now, and they do stuff with him ( which I dont need to know about) and stuff at home ( which he does not need to know about). They do a good job of enjoying both sets of parents and their new partners without involving anyone else.
He was a lousy cheating husband and a dreadful liar and a pretty much absent dad, but I recognise that they want to see him as much as they want to see me. We just do it separately.
Honestly, I've no desire to see him or attend any event where he is present, as he's very much a stranger to me, I've no longer any rage, happily remarried now, but out of respect for other family members we no longer attend 'joint' family dos. He does his family thing, We do ours. Neither of us would dream of attending anything jointly.
I did not attend his parents funerals but sent a card to his family expressing my sadness and sharing some happy memories of them.
I suggest that you and your family accept your MIL pain and distress as it is deep and long lasting. Arrange separate opportunities for meeting with FIL and MIL independently, not two parties for everything, just invite MIL to meet the baby before FIL , not on the same day, but for coffee. Alternate invitations to parties. Christmas etc. Agree with your other family members a system and stick with it . It works well for us here. I didnt expect an invitation to his parents funeral ( although they were my in laws for 25 years and I loved them dearly) nor did I invite him to my wedding last year. None of his business!
Separate people seperate lives will make it easier for everyone, the expectation that they can all just move on and be civil now just isnt the case, clearly nor might it ever be.Joint family events are over now their marriage is over, regrettably I think you must accept that both of them at the same event isnt good. Organise and invite one to one thing, one to another.
I am happy without being any part of my exes life, but happy for my children ( and future grandchildren) to be part of his life if that is what they need. He does not deserve their love and attention, but it is important to them, so I let them get on with it without involving me. I am healed and happy, as are my teens by running two happy seperate household events.
I personally dont like that my teens call her family granny and uncle x and nephews y, as they really arent, but this isnt those.peoples fault and they are in their lives and must call them something. I cant insist or micromanage this so I.let it ride. Seperate lives, much easier.
My advice to you all is to accept that joint family events where both will attend, that time is over. Arrange seperate events for MIL to do special things with you and her grandkids. ( not two 18ths, two christmases etc) and ensure that both FIL and MIL have equal opportunities with you all, but separately. We are all quite used to this arrangement here and it's quite 'normal' now .
I feel for you all, but this solution has definitely worked for our extended family.
Finally, Be aware of social media though. I dont want to see his holiday pictures, his Christmas with my kids or their party they threw for a christening, wedding or 18th.
Help your MIL to clean up , block and delete those contacts. So she doesnt feel she has been left out from celebrating and encourage her to be involved in organising some of your family events, but ask family and friends to be mindful of what pictures they post.
For example, for my sons 18th I posted a pic of his cake and a few pics of him and his friends. Didnt include any family so no one feels omitted.