She could have been naturalized under her father's naturalization. After age of 18 she could applied for citizenship herself. With law changes in the 1920s, she could not get naturalization through marriage.
Did you look for a naturalization petition under your mother's name? I would do so before assuming that she not a citizen.
Secaucus NJ USA
HASSMAN, SONENTHAL, DAUERMAN, LUCHS - Drohobycz, Ukraine
HIRSCHHORN, GOLDSTEIN, BUCHWALD - Dolyna, Ukraine
ELLMAN, COIRA, MAIDMAN - Minkovtsy, Ukraine
KAGLE, FASS - Ulanow, Poland