It was August, and Gina Rinehart was preparing for another school year as a special-education teacher in Hemet, Calif., when she got the call: Her father, Floyd Hall, was facing surgery to remove a tumor in his lung.

She flew to rural Lake Cushman, Wash., to be with her parents, expecting to spend two weeks helping her dad recover. Her father, known as Bub and an active retiree at 68, spent his days woodworking, volunteering at the local food bank and helping his own 95-year-old mother.