Although she was painted often, especially by St. George Hare, there is little about her. Her article in thepeerage is here.
This comes from a Wiltshire government site, "Lady Alda Annie Hoare was the wife of Sir Henry H. A. Hoare and they were also cousins. She was a great grand daughter of Sir Henry Hugh Hoare and the daughter of Purcell Weston and Alda Lethbridge (who was the daughter of Sir John Lethbridge and Julia Hoare). They were married in 1887 and succeeded at Stourhead in 1894, making many improvements to the house and grounds during their long tenure of the house. They had one son, Captain Henry Colt Arthur Hoare, who died of his wounds in 1917. Henry and Alda died within a few hours of one another on 25th March 1947. There are obituaries, which I think will be mainly about the life of Henry, in the Devizes and Wiltshire Gazette for 3rd April 1947 (page 5) and in the Times for 17th April (page 7). Alda Hoare revised the Guide to Stourhead in 1930."
Letter from Britain has this, "Their only son, Harry, was a sickly boy, but still went to fight in the First World War. Tragically he was killed following a battle in Palestine. His parents were devastated. With the loss of their heir, plans were drawn up to give the estate to the National Trust..." According to The Joy of Slow Communication, she corresponded with Thomas Hardy and his wives Emma and Florence.