Stack was born in India, the daughter of a Sandhurst-trained 8th Gurkha Rifles officer, Captain Edward Hugh Bagot Stack (1885-1914), and his Irish wife, Mary Bagot Stack. Her father, born in Shillong in 1885, came from a line of Britons who had served in British India, her paternal grandfather having been the Indian Civil Service officer Edward Stack. At the onset of the First World War in 1914, her father was posted to France, while Stack and her mother embarked on a voyage to England; by the time of their arrival, news had arrived of her father's death in action at the Battle of La Bassee. He is buried in Nord-Pas-de-Calais, France. 
In 1938 she married Lord David Douglas-Hamilton with whom she had two sons, Diarmaid Douglas-Hamilton and Iain Douglas-Hamilton. Douglas-Hamilton, then a squadron leader in the Royal Air Force, was killed in 1944 when his damaged airplane crashed, following enemy action over France.
In 1950, Stack married the surgeon Alistair Albers in South Africa. Albers died in a climbing accident in 1951, while climbing Table Mountain accompanied by his wife. In 1964, she married Brian Power, an Irish barrister.
- Veronica Horwell (2 January 2011). "Prunella Stack obituary". The Guardian. Retrieved 12 April 2012.
- "Obituary - Prunella Stack". The Daily Telegraph. 31 December 2010. Retrieved 12 April 2012.
- "Prunella Stack Weds As Police Tackle Mob". The Montreal Gazette. October 17, 1938. p. 6.
- Martin Childs (1 March 2011). "Prunella Stack: The 'perfect girl' of the 1930s who led the Women's League of Health and Beauty". The Independent. Retrieved 12 April 2012.
- Power, Brian. "Brian Power obiturary". The Guardian. Retrieved 24 November 2015.