His parents: Joseph and Rebecca (Lax) Smith
Robert H. was born about 1846 or 1847 in Henry Co, TN.
I have resisted identifying him as the Robert Smith who went several counties east from Henry County and married a woman there, but the social security record of their son Jake Tate Smith was persuacive.
Since Robert's family was next door to Catherine and her family in 1880, I believed it somewhat likely that her orphaned children joined his and his wife Martha's family; howeverI cannot find more on anyone in the family except Jake Tate after the 1880 census.
1870 Census Wilson Co, TN, 2nd page of 561 or 1st page of 562 (unsure of labeling): Robert Smith, 21 TN, Martha Smith, 18 TN
1880 Census Ripley Co page 526C: family of R. H. Smith, 30, TN TN NC, Martha, 27, TN TN TN, J. E., male 9 TN TN TN, M. E., female 6, MO TN TN, J. T., male 2 MO TN TN
From US National Archives at https://aad.archives.gov
Jake Tate Smith, born 15 October 1877, Doniphan, MO (spelled Donithan on record); parents Robert Smith and Martha E. Tate; issued June 1937
Marriage license #257, issued 1 Dec 1869, Wilson Co, TN: Robt H. Smith and Martha Tate; rite performed 2 Dec 1869 by R. ?? Campbell JP