I have been researching your Jesse Taylor for a couple of days. I think I have, at least, gotten a fair picture of the family members and where they came from in Tennessee. None of this may be new to you, especially since you posted some years ago.
Jesse, I believe, was in Perry / Decatur County (Decatur being created from part of Perry in 1945) Tennessee, from at least 1830. I found him with his first (?) wife Catherine in 1850, and an 1840 family that fits nicely, too. In 1860, he appears to have second wife, Emily R. and in Spring of 1870 the family moved to Brazos County, Texas.
I do not see a perfect fit for your Kitty having a first name of Sarah, as there was already a daughter by that name. Additionally, there is another confusing Sarah in 1880. What I have cobbled together (birth years are approximate, they are only based on ages (which are only loosely given) in the censuses.):
Jesse Taylor, b. 1804, South Carolina
Jesse moves to Tennessee.
Jesse marries Catherine ------ abt 1828, she was born abt 1808 in North Carolina
Jane b. 1829
Susan b 1833
Daughter (also between 5 and 9 in 1830)
Son (both under 5 in 1830, one of them may be James)
James b. 1840
Paton (son) b. 1842
Sarah b. 1844
Thomas b. 1845
(**Thomas and the earlier children would have been said to have been born in Perry County, Tennessee. The later children may have been born in the same home, but it would now be called Decatur County, Tennessee.)
Catherine b. 1847
I think about 1852 or so, Catherine dies and about 1853 Jesse marries Emily R --------, b. 1835 in Tennessee. This death/remarriage date is only based on a gap in children's births which could be also explained by children missed in the records (infant death. But by the 1860 census, Catherine is replaced by "E.R." - named as "Emily" in 1870)
Jesse, Jr b. 1854
Eddy (son) b. 1858
Florence b. 1862
Albert G. b. 1863
William b. 1865
Mary Elizabeth "Mollie" b. Apr 1868 (she m. William Turner Alexander Moss [thus into my family, and how I started looking into where she came from.)
Samuel b. abt Mar 1870 (Decatur County, Tennessee)
Spring of 1870 the family moved to Brazos County, Texas. They were there for the 30 July 1870 Census.
Erma S b. 1872
-Between 1870 and 1880, 2nd wife Emily dies and Jesse marries his (at least) third wife, Mary Kennedy b. 1929 Alabama. In the 1880 census, the family includes "B.F. Kenody, 50, b. Alabama, school teacher, brother in law to Jesse."
Jesse dies 9 Jan 1884, as stated in the obit you reference.
--Worth noting: I am confident that the Brazos, TX Taylors are the same at the Decatur, TN family cited (there appears to be another Jesse Taylor in Decatur County also, fyi) along with the frustratingly slight overlap of children's names/initials, in 1860 (TN) there was a 9 year old boy, "H. Davis," with the family on the census ("inmate" written in the margin-- I am inclined to think this means he may have been an "inmate" of the orphan house, or similar.) In the 1870 census (TX) there is also, now a teenager, "Henry Davis" (white, and b. Mississippi) with the family.
I am amazed at how little further information I have been able to gather on all of Jesse's children! I did find an article stating that the Decatur County courthouse (wait for it.....! ) burned down in 1869, but many of the children would have been leaving their trails in Texas, anyway.
Well, I hope something here will have been of interest to you, or someone else. It has been an interesting puzzle, even if not closely tied to my own family.
(my tree is "Yanceys, Booths and Beyond" if you want to look at my research results.)