I'm so glad you posted this query.I've been trying to figure out Thomas Otis Poulter for a long time, and the strange thing is, nobody in Harrodsburg that I have found seems to have the answer.Look at the following and see if you think this could be the family.
Descendants of William R. Poulter (1818-1898) and Eliza Ann McRay
a. Emily Poulter, b. 8 Oct. 1841, d. 16 Apr. 1896, m. J. M. Hieronymus.They had no children.
b. Mary Poulter, b. 19 Sept. 1843, d. 22 Jan. 1916, m. as his second wife, 11 May 1886, Mercer Co., Ky., Benjamin R. Ransdell.They had no children
c. Marion Poulter, b. 8 Sept. 1845, d. 1919, m. Annie Miller, d. 1888, Johnson Co., Indiana.They had no children.In 1910 he was living with Nancy and Mary in Mercer Co.A "brother" Wm. is listed with them, but he was born ca. 1885.
d. Sarah Poulter, b. 18 Apr. 1848, m. 16 Sept. 1869, E. P. Haymaker, b. 25 May 1843, Christiansberry, Va.They do not appear in Mercer Co. in 1900 or 1910.
(1) Zera Allis Haymaker, b. 13 Aug. 1870.
(2) William P. Haymaker, b. 4 Feb. 1872.
(3) Charles O. Haymaker, b. 21 Feb. 1876.
(4) Lillie Haymaker, b. 26 Jan. 1879.
(5) Clarence Haymaker, b. 14 Aug. 1883.
e. Hiram Poulter, b. 29 Aug. 1852, Duncansville, Mercer Co., Ky.Not in the 1860 census.
f. Nancy J. Poulter, b. ca. 1855.
g. Maria E. Poulter, b. 24 Jan. 1857, Salem Church, Mercer Co., Ky.Not in the 1860 census.
Would you please not only answer this on the forum but also send me an e-mail.I will have some more questions for you, if you don't mind answering.