Her daughter Marcia Davenport was the child of her first marriage (to Bernard Glick, an insurance man). Gluck later married Violinist Efrem Zimbalist and had two children, Efrem Zimbalist, Jr. (1918–2014) and Maria. Gluck evidently adopted her professional surname as a variation of her first husband's surname ("Glick").
Gluck retired to New Hartford, Connecticut, to raise her family in 1925. Although by background an assimilated and nonpracticing Jew who continued to consider herself ethnically Jewish, she found herself attracted, along with her husband Efrem, to Anglican Christianity, and they regularly attended the Episcopal Church in New Hartford. Efrem Jr. and Maria were both christened there, and the couple placed Efrem in an Episcopal boarding school in New Hampshire. Efrem Jr. later became active in evangelical circles and was one of the founders of Trinity Broadcasting Network. Gluck recorded several Christian hymns in duet with Louise Homer, among them "Rock of Ages", "Whispering Hope", "One Sweetly Solemn Thought", and "Jesus, Lover of My Soul".
After a long illness, she was taken to the Rockefeller Institute Hospital in Manhattan, New York City, but died from liver failure several days later, at 9:30 am on October 27, 1938, at the age of 54.