Sorry, that'd be it for me.
Your ex is violent and abusive. You have good reason to want to protect your child from that. By that reckoning, your MIL isn't prepared to protect your daughter from violence and abuse.
If you can't trust her on this very biggest thing, there is no trust at all. There is also no respect - how dare she make this decision for you and your daughter?
I would be angrier than angry, and it wouldn't be the kind of anger that would blow over. She's shown you what she thinks of you and your daughter as a family, an entity to be respected and cherished - nothing. She's shown how little regard she has for what you have done, the steps you have taken, in maintaining contact.
I would be cutting contact for the foreseeable future, and telling her why. She does not get to make those kind of decisions for your daughter. If she thinks that she can, then she isn't grandmother any more, never has been.
If she's prepared to put her son and herself ahead of your daughter's wellbeing, that's all you need to know.
I'm not sure that supervised contact (I'd be too angry to have her in the house tbh) would work in this situation - above all, I'd want to get my point across by making it utterly clear to her that she has crossed the biggest line she could. She'd have a hell of a lot of grovelling to do before she even saw my daughter again, and the aim of that wouldn't be to punish, it would be to make her realise, absolutely, how out of line she was, and if there was a second chance, to make SURE she never even dared to think about doing something like that again.
However. I don't think I'd give a second chance, simply because I think that give it a year or two and your daughter will be being asked to keep secrets from you, will be taken to see her father, and from there on it's a slippery slope.
Sounds like your instincts about this family were spot on. Do you want your DD to spend family time here, become normalised to it?