Maybe a copy of her marriage to Fred Faulkner will have some valuable information for you.

I noticed that Fred Faulkner was not only her husband, he was also the County Judge as you will see in the application which is attached here.

I found two obituaries. One for Hattie, the other for her Father.

Walter Carroll died in 1956
Publication:
Ardmore Daily Ardmoreite March 26, 1956

Hattie Faulkner died in 1969
Publication:
Ardmore Daily Ardmoreite September 5, 1969

Sorry, no death certificate.