Everybody is wrong. Continuing behavior like this, there will always be more tension among these people.
My guess is that the MIL is not going to change. That being the case, my suggestions to this group would be:
1. For the daughter and her husband, keep your time with this woman at an absolute minimum.
2. For the daughter and her husband, since your mother/mother-in-law will not curb her behavior, you step up and be the adults in the room. She is trying to goad you into fighting. Don't take the bait. If there were a future situation like this, he could respond with, "Thank you for letting me know," or, "Yes, I agree with you. It was very generous. What a great guy he is."
That would be a better way to shut the MIL's mouth.