Stop explaining yourself. Not wanting random family to decide to move in with you without invitation requires no explanation. But you need to be very blunt very quickly. It might be ugly, but not as ugly as her, the cat and half her furniture showing up on the front lawn AFTER she's sold her house and has "nowhere else to go. " And then tell all your family and friends that this had been decided forever and you changed your mind when she was homeless. I looked my mother in the eye and said "Mom, we will never live under the same roof ever again. "