It is my opinion and belief, based on the census record below, that your Rush Crowe was the son of William Carroll Crow and his first wife, Lotta.I am told that Lotta died in 1915 and William Carroll Crow remarried to Esther Edna Hossfield after 1920.
Year: 1920; Census Place: Prairie, Hot Spring, Arkansas; Roll: T625_63; Page: 2A, dwelling 33, family 37 Johnie Crow age 70 Head SC SC SC (Jonathan C. Crow) Elizebeth Crow age 67 Wife TN TN TN (Elizabeth Allen) Floy Crow age 16 Granddaughter AR AR AR (Flory M. Crow) Cecil Crow age 7 11/12 Grandson AR AR AR (Cecil R. Crow) Rush Crow age 3 4/12 Grandson AR AR AR (since mother, Lotta, died in 1915, birth date is wrong on ancestry.com index and is blurred on original census, so I assume Rush was born before 1915.)
Same dwelling 33, family 38 William C. Crow age 47, widowed, AR SC TN (Wm Carroll Crow, husband of Lotta, son of Jonathan & Elizabeth Allen Crow).
Memorials for William Carroll Crow and both wives are posted at Fina a Grave, Neighbors Cemetery, Midway, Hot Spring Co., AR, memorial numbers, 5296187, 5296212 and 5296183. Wm C. Crow's parents are also buried at Neighbors Cemetery.
If this turns out to be your Rush Crowe, then we are distantly related.
These are Gold DNA Crows of South Carolina and beyond. firstname.lastname@example.org