Could this be my great-great-grandmother's family?

The most frustrating brick wall in my tree is currently my 2nd-great-grandmother Mary Alice Cain Read. I have tried just about everything to look for her, from going page by page through the census in Barren and Warren Counties in 1880, to pulling her death certificate from 1955, to looking for siblings in the city directories in Bowling Green in the 1940s & 1950s. I've had no luck in several years of searching through various Kentucky records.

But earlier today I took another long look at the note written by Guilford Dudley Read granting his permission for Charlie Read to wed Mary Alice in February 1895. Perhaps her last name was spelled Cran[e] on the note. Perhaps she spelled her name as Mary Alice Crain instead of Mary Alice Cain.

I looked again at the 1880 Census. About 20 miles north of Glasgow, Kentucky lies Hardyville, Hart County, Kentucky. And in 1880, a two-year old, born approximately 1878, with the initials Mary A. Crain is listed as living in the household of John K. Crain and his wife Martha. Is this the family of my 2nd-great-grandmother?

If any others are researching the Crain family in Hart County, Kentucky and stumble on this page, and happen to have information on this Mary A. Crain, I would be interested in knowing more.