I am also doing research on the Martha Washington mentioned in Helen Keller's autobiography. I came across this a letter from the Helen Keller Archives at the American Foundation for the Blind that may be of interest to you. It is from a Mary Vinson who says she was the child who played with Helen, and that her mother was the cook, named Jessie Hart (perhaps with a different last name later?).

https://www.afb.org/HelenKellerArchive?a=d&d=A-HK01-03-B088-F02-017.1.1&e=-------en-20--1--txt--mary+vinson------3-7-6-5-3--------------0-1