There is definite confusion about the daughters of Henry. I not sure this one who married a Bullington is the daughter. Elizabeth "Hulda" Pippin Chaffin was listed as deceased in the settlement of her parents' estate as was Eliza Pippin, unmarried, no issue. There is always the possibility the Elizabeth Chaffin Bullington had a second marriage to a Chaffin.
Elizabeth "Betsy" Pippin and Joseph Bullington were married in March 1858. Joseph Bullington was born in 1838 in Jackson County, Tennessee. He died in November 1884 at the age of 46 in Nashville, Davidson County, Tennessee.
Joseph enlisted in 1863 in Cookeville TN in Company K, 8th [Dibrell's] Regt TN Cavalry, Confederate. Late in the war this regiment served as President Davis's escort and surrendered at Washington, GA, 2 May 1865.
The family lived in Davidson Co TN at the time of the 1880 census. Joseph died in Nov 1884 when he was kicked in the head by a mule. Elizabeth moved to Texas with several of the children. They had nine children.