That is straight up weird and creepy. I would never ever again trust my child to be unsupervised with someone like that. I am trying to think up an explanation in my head of what exactly she was digging for that would maybe make some sense...like curiosity about your finances or something (that still would be totally inappropriate but less creepy), but she was digging in your dirty laundry too. That is bizarre and borders on some sort of weird fettish/obsession. I don't know what but it just is "off." Plus, your DD trusted you enough to tell you what was going on and she obviously felt very uncomfortable, so I wouldn't give granny the chance to make her feel that way again. Granny broke trust and lost her opportunity for that sort of relationship with your DD because clearly she isn't stable and cannot be a positive adult in your DD's life.
Also, I will just say that I hear a lot of people saying that they want their kids to have a relationship with grandparents despite the fact that they themselves have enough issues with grandparents that they don't want a close relationship with them. I really don't think kids suffer one bit from not being close to grandparents who lack boundaries, yell and scream like you describe, etc., and this is coming from someone who wasn't allowed to have a relationship with certain toxic grandparents. I did not miss a thing. I am glad that they weren't part of my life.
I agree with others who say only supervised visits here and there and not at your house. Your MIL doesn't sound like the type of person any of you need to be spending a ton of time with. Good luck!