Well - I am going to take a bit of a dogmatic view here. Christmases with little children are very precious, both to them and to you as their parents - there are so few of them when the little ones believe in Santa and are awed by the magic of the twinkling lights etc. That is your priority at the moment - to make Christmas as special as possible for the children. Childhood is too short and cannot be wasted. It is not going to be special with MIL breathing down your neck, given the history.
I spent just one Xmas with my in-laws and vowed we would never do it again, especially if we had children - and we never did - it was just too grim and I wanted my children to have happy magical memories. We did not fall out with them, we were just clear about our priorities.
So....I think you need to say to this lady (face-to-face, by email, by letter - however you think you can manage) that Xmas is a very special time for the children and you want to have that as your absolute priority - to make it magic for them. Tell her she is very welcome if she can share that priority, that you know she has some problem with you (having heard the phone conversation), but that you want that to take a back seat for the sake of the children. If she blows a fuse, you will know it will not work and you will have to say no to her wish to be there.
Now - the other alternative is for you to grit your teeth and be as sweet as you can - but you will setting a precedent for all the Christmases of your children's magic years, and they will never have a Christmas without you being on edge.
I would be inclined to try and stand up to this lady - appeasement is not always the best answer if children are involved and will lose out. There is no need to start a row, but you cannot undo the experience of the phone call and she cannot expect you to pretend that it did not happen.