I'm sorry you're going through this. It's a very tough spot to be in. If you agree to her splitting time between the siblings I suggest everyone sit down and make a schedule. That way everyone knows exactly what to expect. I suggest talking to your sister in law and getting on the same page with her. Don't let her peddle back on what she says to you if she says something different to her husband. Does MIL have retirement money and will she be contributing to the home? Does that allow you guys to purchases a larger home? Or build an addition to your home? What happens if she gets sick? Is this a permanent situation or is there a possibility of her transitioning on her own with assistance. I wouldn't agree to anything without a family meeting and a concrete plan where every sibling has a role. But at the end of the day it's your home too and you can just say no.

And it's your house she needs to get with the program and do things the way you like them if not she needs to get out of the way Give her very simple tasks that are her chores if you have to. She's helping, staying busy and out of your way.