Authorities confirmed the death of Anne Bury, 56, who lived in the North Yorkshire village of Swainby, and said her son, Alex, remained in hospital. Ms Bury's mother, Cecilia Bury, in her 80s, has been discharged after treatment.
The Britons were allegedly shot by the gardener at their holiday villa in the resort of Dalyan while celebrating Anne Bury's 56th birthday.
Turkish TV footage showed detectives searching the property, where balloons and other evidence of a celebration were still visible.
Reports said the gardener had argued with the family, who reported him to Turkish police. He was detained, but on his release headed back to the villa and opened fire.