Do what you think is right for your family.
Nope not at all. I wouldn't have my MIL around if I were you. You need to be comfortable in your own home. Tell her to get a hotel/B&B near by but she cannot stay at your home.
You're not wrong! If you aren't comfortable with it than she needs to stay somewhere else. Bnb, hotel, etc. Doesnt matter how far her dementia is, its no fun for anyone involved. BUT it's not an excuse to put up with abuse in any capacity from the person with dementia, or anyone trying to justify them. Even early dementia patients can have violent spells and be cruel when they never have before.
Your not a jerk! U have every right to feel the way u do towards her if she makes u uncomfortable then voice it put your foot down and if your partner doesn't stand up for you then he's just as bad as her. There are facilities that help with dementia and take care of them she can stay there
No you do whatever you are happy with, people can sit back not actually knowing your mil not knowing you or your situation and judge and say you should do this, I'd do that but it's your choice do what's right for you
You need to do whatever makes YOU comfortable. While yes, i understand people saying that with her starting to show signs of dementia it might be better for her to stay with y'all, you know what will work best for your family and you really don't need to risk your nanny leaving or giving your daughter an eating disorder at this young an age