Sibling rivalry has helped Fariborz Ghadar, 69, and his sister, Margaret Ghadar, 65, grow closer—and healthier. For the past three years, the two have met regularly for squash dates in Washington, D.C. “The beauty of playing with my sister is that I can’t stand her up,” Dr. Ghadar says. “She’ll get really angry if I don’t keep my commitment.”

The siblings attended universities in Boston and played squash together in their 20s. After graduation, Ms. Ghadar went on to become a vice president at J.P. Morgan in New York City...