Good lord, some of the posts on here are ridiculous. And I really doubt if some of the more “hardline” posters would actually do what they are encouraging op to do. I think it is either that they enjoy the drama or are being ‘keyboard warriors”.
I don’t condone smacking children. I don’t think a sharp tap on the hand to make a point to a particularly recalcitrant child is abusive, damaging etc, and I wouldn’t mind if my mother had done it to my DC if they were being very naughty or to stop them doing something dangerous- but I do recognise that many parents wouldn’t do like it. A tap- when it is a genuine sharp tap, and not done with much force, is different to being beaten/hit/punched- but as I say I recognise others feel differently and would never lay a finger on anyone else’s child.
All of that said, I do think the sensible and reasonable thing to do- given that OP’s mum has no history of being abusive, though clearly is struggling to manage young children given OP’s brothers have also noticed that she seems to lack patience with their children- would be to sit her mum down and have an honest and frank discussion about what happened, explain that op and her husband will not tolerate any physical chastisement at all and ask her to respect that. Unless her mother has a history of deviousness or ignoring OP’s requests, that should be sufficient. Along with perhaps being more aware of her mother’s limitations and only request childcare accordingly. There is absolutely no need to jump to “never allowing her to see the children”, going low or no contact or refusing to ever leave her in a room with children without supervision. That is how you destroy relationships, possibly within the wider family too, and I strongly suspect that OP’s mother would bring much that is positive into the lives of her grandchildren, losing that over a situation that can easily be addresses is absolutely ridiculous.
My own grandparents definitely chastised us at times- though I don’t think ever smacked me, definitely did get a sharp tap to the hand on occasion (once to stop me putting my hand into something dangerous) and were stricter than my parents. We worked out that there were different rules at granny and grandpa’s than at home. It wasn’t confusing or distressing. They were lovely, warm and caring people who adored us. We had a wonderful relationship and my grandmother remains is one of my favourite people- I still miss her. Had my parents cut them out of our lives/reduced their presence in our lives for one (relatively minor) transgression, without even speaking to them about it, I would not have had the love and support I got from my grandparents and my childhood (and adulthood, for that matter) would have been the poorer for it.
OP- just speak to your mum. She’s your mum, for goodness sake- it’s ok not to agree with what she’s done and even to be upset by it- but communicate that to her, ask her not to do it and move on. Obviously, if she ignores your wishes again, then you need to address this issue more significantly, but give her the opportunity to explain what happened, understand your point of view, and the opportunity to make it right.