I think Sarah Mooney Smith's mother is Sarah Faulk, not Mary Faulk. I understand that the death certificate says Mary, but hear me out.
In 1850, Sarah and John R. Mooney are in Pike Co. AL with children John, 2, and Lurana (indexed as Susannah) 6 months.
In 1860, Sarah and John R. Mooney are in Wood Co. with children Elbert, 12, Lurana 10, Martha 8, John, 6 and Elizabeth 1.
In 1870 Sarah and John are in Wood Co, with children Martha C., 17, Mary L. 6, Sarah R. 4, and Susan 3. Interestingly, they are in the same household as Enoch and Anna West, who are slightly younger than them.
In 1880 Wood Co. , John R. now has a wife named Mary. This is not Sarah, as also in the house hold are John's children Sarah R., 14, Susan A., 12, Joseph A. 8, Livey 7, and TA DA! step-children, (Mary's children), Levi (?) Littletonand Mary J. Littleton, 17.
I found Sarah Mooney Smith's sister death certificate (Mattie Mooney Perkins), who says her mother is Sarah Faulk. Mattie was b. 1852, Pike Co. AL, d. 1923 Denton Co. TX.
It is entirely possible that Mary is related to Sarah, either a sister or cousin.
Checked your posting history and looks like you have done a great deal of work on the Faulks from Pike Co. Do Mary and Sarah not fit in?
There are quite a lot of Faulks all around J.R. and Sarah in Wood Co. And there are some other Mooneys as well.
Anyway, I hope this helps in some small way. Good luck! Andrea (no relation, just a volunteer)