Personally, I would let my MIL stay in that situation - she is family after all and is in need of assistance. I would be doing everything in my power to either allow her to move in (e.g. by setting strict limits on how long she can stay, ground rules in the house, etc) or say no and see if you can be of assistance in other ways (e.g. financially, or helping her look for work/somewhere to stay). In your situation it sounds like you would really rather her not stay with you and given it could potentially impact your relationship with her and your mental health/stress levels maybe the second option is better?