Did you ever get your question answered about Solomon Kessinger III's son, Thomas Kessinger? If not, maybe this will help. (See: Hart Co. census of 1850 and 1860)
Solomon Kessinger III was born in 1815 in Kentucky.He married his 1st. wife, Rebecca Fenwick (B1824-D1860 approx.) Their children were: Peter (1840), Lucretia (1842), Miles (1846), Thomas L.(1851), Solomon Kessinger IV (1854 in Hart Co., Kentucky)
Solomon III married his 2nd. wife, Elizabeth Tharp (B1849)in approx. 1866. Their children are, as Mr. Kessinger listed in his reply to you. Their 1st. child was Robert Lively Kessinger (B May 15,1867) (See:Hart Co. census of 1870 -- Elizabeth is listed as 21 years old).