As far as allowing her in your house - I'd stand firm on that. I have a crazy "SIL" too. Not quite as crazy as yours, but pretty crazy. She actually ended contact w/ all of us for about 5 years. It was WONDERFUL. But now she's coming back around...
Anyhow - your home is your home and you don't have to invite anyone over that you don't want to.
Just be aware, though, that as far as your kids go, if your IL's aren't going to take as firm of a stance as you, then this may mean that you all have to make the choice to miss out on family get togethers that aren't at your house. As much as it sucks, it is everyone elses choice to maintain a relationship with her.
If you're o.k. w/ doing this so that your kids aren't around her - then have at it! I'm just mentioning it from a "this may be what it means" place.
As far as why your FIL may not be taking a firm stand - for as crazy as my "SIL" is, it's still BIL's choice to be w/ her. And in an effort to show BIL support, my IL's accept her. It drives me insane because they act like she's done nothing, but.... they do it for their son. Not for her.
And my BIL is also FULLY aware of her craziness, aware of our issues, etc. Recently, DH out an dout asked him "why are you with her?" and he said "I don' tknow. My friends have asked me the same thing". ??!?!?!?!? REALLY? But -I think it's just easier for him to stay than leave. It's insane. But it's his choice.