Hands down the mother! Kids are not entitled nor is it a law that kids or anyone inherits anything. They want to keep the house buy it off the mother at market price so she has money to live on that her and her husband worked for. You work to provide for yourself and family. Once they reach adulthood they support and make their own money for retirement just like their mother and father. If the mother stayed in the house and wound up in a nursing home, the nursing home would get the house anyway to pay for the outrageous monthly cost. Let the mother enjoy her senior life without fear of losing her children’s love or running out of money.