I have a MIL who is prone to putting her foot in her mouth and it has stopped me from seeing her, which means she doesn't see DS either.
Right from the start she was the sort of person who 'speaks before she thinks' etc but she is also quite manipulative and likes everything her own way. If things were not as she wanted them, she would cry and FIL would shout until things were as she wanted them.
So for six or so years of my relationship with DH I had an up and down relationship with PILS, mostly we got along and I either tried to accommodate them for the sake of peace and let things go or ignored my hurt feelings for the same reasons.
And then we lost a baby to stillbirth and MIL was utterly cruel. In the guise of speaking before she thought, she argued with me about the time he was born, demanded to know when we were going to try again and then asked me if it still hurts to give birth if your baby is dead. All of this just three days after he was born. The night before our sons funeral she accused DH of being 'moody' and 'not sounding happy enough' to speak to her.
And she went on like this for the next eleven months, when we lost our second child to prematurity. And she promptly accused me of having something wrong with me, dismissed our children as 'not proper grandchildren' and went on to wonder if our baby, being premature, was born with a whole face or not.
Comments like that went on for two years, mostly whenever we were alone. Which I think shows there was a bit more thought to them than she claimed.
DH finally spoke to her and she told him she was sorry, but she never apologised to me. Instead she got worse and started to tell lies about me to the wider family and still getting in some cruel/thoughtless comments and some weird, stalkerish behaviour that made me ill and left me feeling like a prisoner in my own home.
We had to move to the other side of town, which actually still isn't far enough. BIL and SIL, who were also on the receiving end of some very intense behaviour, actually emigrated to the other side of the world and admitted the decision was helped by the way PILS behaved towards them.
And it was then, ten years after I married DH, that I finally cut them out of my life and DS's life. DH sees them occasionally but even he admits he dreads going most of the time because they are always so miserable and negative.
Anyway, my point is, you might not know the half of what has gone on, especially if your SIL managed to live with and get along with your mother for a time. Nobody wants to feel that their parent might be capable of this sort of behaviour, My DH still has this idea that things could be different if I would give his parents a 'second' chance, when in reality they have had more 'second' chances than I can count.
And I suppose it could be said that I was the one to withdraw from them. DH's family has a hard time admitting that it's because PILS push people so much. You have no choice but to back off when someone is constantly in your face pushing you back even as they try to grab hold of you and pull you closer.
Maybe it's not been like that with your Mum, perhaps it is your SIL. But perhaps it's not and at the moment all you have to go on is the comments your Mum made years ago and the fact that your DB repeated them to his wife at some point.
So the chances are, I feel it's most likely to be one of these three things. SIL has been bearing a grudge about those comments since they were first made and they have eaten away at her relationship with your Mum. Or SIL has only found out about those comments more recently and has felt shocked and upset to learn what your Mum thought of her, especially as they got on so well when they lived together, and has reacted by cutting your Mum out. Or your Mum has said and done other things, perhaps without thinking, that have broken down her relationship with your SIL.
You might never know which it is, one of those or something else. But please don't get involved. Having the wider family get involved with my estrangement from MIL has only made things much worse, it made it more difficult to repair things when things could have been repaired and now it's too late for that it's left my other relationships with DH's family strained, which has impacted on our DS too. And that's not what I wanted at all.