Dear James,
Though it won't help for her maiden name, I think her husband may be Eli Barton. There are two listings in the 1850 census, and they have been married within the year.
"United States Census, 1850," database with images, FamilySearch (
https://familysearch.org/ark:/61903/1:1:M4LV-KGB : accessed 21 April 2016), Eli Barton, Yalobusha county, Yalobusha, Mississippi, United States; citing family 930, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
"United States Census, 1850," database with images, FamilySearch (
https://familysearch.org/ark:/61903/1:1:M4L4-VPM : accessed 21 April 2016), Eli S Barton, Chickasaw county, Chickasaw, Mississippi, United States; citing family 774, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
Hope this helps! -NGP