Not sure of connection with the George Abbott family. Much of the remaining information is consistent with my Ancestry tree posting.
1930 census of Zanesville, Muskingum County OH includes FNU(likely Cecil) Kinney, 47, b OH, conductor, railroad, Mabel, 42, Mildred, 23,teacher, day nursery, Helen, 19, Paul, 16, and mother-in-law, Julia Abbot(sp Albot), 74, b OH, parents b OH/PA, widow.
Ohio vital records show a Mrs Julia Abbott b 27 Dec 1855/OH, d 20 Feb 1931 in Zanesville OH. Husband not listed. Parents listed as Lewis Stevens and Sarah LNU. Informant was Mrs. Helen Kinney, 633 Putnam St, Zanesville OH. Seems likely this Julia Abbott is mother of Mable Abbott, since age is consistent with 1930 census.