Since we have no exact birthdate and the Harrington family came to Pomfret, Chautauqua, NY at about the same time in 1817, it's hard to tell where Harriet was born.
She was married ~1836 & with family in Arkwright, Chautauqua Co, NY in 1840 Census.
Still married and living with family in Wayne, Erie Co, PA in 1850 Census
Lives with daughter, Medora Viola Cochran, in Ballville, Sandusky Co, OH in 1860.
Other family trees say she divorced Andrew, sometime after 1857. Quote from archived WC tree -
http://awtc.ancestry.com/cgi-bin/igm.cgi?op=GET&db=*v104t1662&id=I258
"From a diary Harriet kept, she says Andrew left for parts unknown January 3, 1857. Apparently they were divorced at a later date and Harriet married again, to a man named Hiram Harrington." [ I believe Hiram was her youngest brother who had also abandoned his family at the same time!]
The Fremont Weekly Journal of Fremont, OH ( local PO to Ballville ). "Harriet Harrington" named in letters remaining at the Post Office, 17th of May, 1861, and later 15 Aug, 1861.
No record after that. Died probably between 1860 and 1864. I checked the most complete record of obit's in Sandusky, but there were gaps, and did not find her or any Harriet in the 1860's.
1880 Census Andrew J Smith says he is a widower.
This is probably her -
http://www.rootsweb.ancestry.com/~nychauta/Wills/Volume1.htm
"p. 161, Abiram Orton of town of Arkwright, Chautauqua County, New York, died 16 Mar 1837 at town of Arkwright, signed 17 Oct 1836, recorded 15 Jun 1837, court 7 Aug 1837.
"Money, livestock, and income from land, including land deeded by Levi Clough and Betsey his wife to my wife Susan Orton during her widowhood. Remainder of personal property to sister Lilly Danforth, wife of Daniel Danforth of Lafayette, Onondaga County, for taking care of my mother. Money to Benjamin Griswold. Remainder to be divided among these 5: Charles Jackson Orton, Benjamin Griswold, Thomas Orton son of my late brother Thomas Orton, Thomas Orton son of brother James P. Orton, Abiram Orton son of Thomas and Hannah Orton and grandson of my brother Philo Orton. If my wife has a child after my death, then this will is void.
Executor: Charles Jackson Orton
Witnesses: Ephraim Harrington, Harriet Harrington, both of Arkwright""
I believe Susan Orton was Harriet Harrington's sister. Susan Orton was staying with her in Ballville, Sandusky Co, OH 1860
Susan had returned to NY by 1864, so I assume she was visiting her dying sister. After this visit, Susan no longer attended Baptist Church, and told them she now believed in Spiritualism. Could Harriet have had something to do with this conversion?