Repeating some details and mentioning new ones…
Catharine Stover married Francis Jones in Pettis County, Missouri in November 1839
1850 Pettis County, Missouri census
Francis Jones, 45, farmer, Missouri
Catharine, 41, Kentucky
William ?, 20, farmer
Polly, 17
Francis, 14
Jacob, 11
Joseph, 8
Narcissa, 5
Thomas, 1
All children born in Missouri and had the surname Jones
1860 Freestone, Texas census (Fairfield Post Office)
Catharine Jones, 46, born Kentucky
Joseph, 17, Labourer, Missouri
Narcissa, 15, Missouri
Thomas, 12, Missouri
John, 7, Missouri
All children had the surname Jones
So, Catharine was possibly still with Francis, in Missouri, in 1853
According to the image, Catharine only had $54 in “value of personal estate” which, looking at several census pages, was quite low.

According to several Anc*try family trees, Catharine’s/Catherine’s mother’s name was Mary Polly or Mary Jane.
Were William, Polly, Francis and Jacob Catharine’s children?
Or, were the children born to Catharine Stover and Francis Jones (prior to their marriage)?
Or, were the four only Francis’ children?
I think it’s least likely that Catharine wasn’t the mother, as she possibly named Polly after her mother.