Her only brother, Ian Huddleston Abney-Hastings, styled Lord Mauchline (1918–1944), was killed in Italy in World War II, so as the eldest sister, Barbara succeeded to the earldom in 1960.
On her mother's side, she was descended from and heir-general of George Plantagenet, 1st Duke of Clarence.
Her other notable ancestors include Mary Tudor, Queen of France; King James IV of Scotland; William Cecil, 1st Baron Burghley; and Alice Spencer, Countess of Derby.
She married, firstly, Captain Walter Strickland Lord on 5 September 1939.
They had one child: Her second marriage was on 21 November 1945 to Captain Gilbert Frederick Greenwood.