It seems that Jesse Mitchell's second wife was Dorcas Long. I don't know what happened with his first wife and mother of Andrew Jackson and Margaret Jane Mitchell.
From what they have at www.familysearch.orgit looks like Andrew Jackson Mitchell sometimes went by A. J. Mitchell. He may have used his middle name at times. Oftentimes there are genealogy resources in counties. You might want to consider doing a google search for genealogy resources in Allegheny and in Greene county, PA.
Here's some info from 1850, 1860 & 1870 United States Censuses
1850 United States Census
name: Margaret Mitchell residence: Jackson, Greene, Pennsylvania age: 18 years calculated birth year: 1832 birthplace: Pennsylvania gender: Female race (original): race (expanded): death month: death year: film number: 444751 digital gs number: 4204726 image number: 00646 line number: 23 dwelling house number: 165 family number: 165 marital status: free or slave: Household Gender Age Jesse Mitchell M 39y Dorcas Mitchell F 34y Margaret Mitchell F 18y Jackson Mitchell M 13y Jonathan Mitchell M 9y Josephas Mitchell M 4y Martha Mitchell F 2y
1860 United States Census
name: Jackson Mitchell residence: , Greene, Pennsylvania ward: Jackson Township age: 24 years estimated birth year: 1836 birthplace: Pennsylvania gender: Male page: 166
1870 United States Census
name: A J Mitchell estimated birth year: 1837 gender: Male age in 1870: 33y color (white, black, mulatto, chinese, indian): White birthplace: Pennsylvania home in 1870: Pennsylvania, United States Household Gender Age A J Mitchell M 33y Harriet Mitchell F 24y Sarah E Mitchell F 3y Jesse Mitchell M 2y Eliza Mitchell F 10m George Mccullough M 22y