So yes you have heard her already unleashing her way of thinking, her nastiness, on the children in the family.
Just think hard here. I can guarantee - and I think deep down you know - that your mother will be unable to stop herself bad-mouthing you to your children, even in just the form of snide asides.
That does a massive, massive amount of damage. I know because I had a grandmother like that. Divide and conquer just about sums it up.
It is very hard to actually describe the kind of damage that treatment does, because it certainly isn't clear-cut. I DIDN'T grow to hate my gran. I DIDN'T get turned against my mother, because it was clear from even an early age what kind of a person my gran was like.
The best way I can describe it was that I grew up feeling sad and disappointed that I had the type of family I did. I hated the feeling of unpleasantness, of lack of love, of bitchiness that hung around like a cloud. Spending time with other normal families and seeing normal, friendly happy affection between generations and siblings made me feel awkward and confused and very jealous. I basically grew up despising not individual members OF my family, but just 'my type of family'. I only see certain members now because I just can't BEAR for my own family to be brought into that, to continue the 'pattern' of bitchy, spiky ways of communicating and for my own child to see that and learn from it. I want a fresh start for my own life with my own children. I don't miss them at all because I don't ever see that group of people as having been a proper family.
Now that's my experience from having been brought up with a bitchy nasty gran who everyone made allowances for, and a stressed mother who was always trying to please her, in a family who to the outside looked perfectly functional!
Your relationship with your mother sounds several steps beyond that.
Please don't make the mistake of thinking that your children can remain unaffected. They CANNOT. They will LEARN from the dynamic between you and your mum even if they don't see you with her. They will LEARN that family means bitchy, nasty, 'supportive' but actually pleased to see the other fail, crowing, snide, mean.
It's taken me YEARS not to see that as the default for 'family life' and it's so hard to break the pattern and not slip into being the same kind of person to one's nearest and 'dearest' - because that's what you learned when you were tiny.
Please think really really hard about this and DO NOT make your mother's 'grandmotherhood' the most important thing. Far far far more important than having a relationship with a grandmother is your responsibility to give your children good, positive, loving role models for them to form their views on relationships and how they work,so they themselves can have good relationships in the future.