I have a hunch that your Nancy P. Mitchell's maiden name just may have been Wooten, Wootton, or something like that. The reason I say that is that I have been searching for Mary/Polly/Pollie Wooten, who I find living in the home of John H. Mitchell and his wife Nancy. Mary/Polly/Pollie Wooten was the wife of Simon Wooten, and the daughter of Peter Moses and his first wife Margaret. Peter Moses is my direct ancestor, though I descend from Peter's second wife.
The only reason I can guess for Mary Wooten to be living with Nancy Mitchell during the 1850, 1860, and 1870 census enumerations would be if Mary were Nancy's mother.
Mary/Polly/Pollie Moses Wooten was born in 1791 in probably Buckingham County, VA and died June 30, 1882 in Appomattox County, VA. She appears to have had a son named John H. Wooten.
Other spellings I have seen for the Wooten surname are Wootten, Wooton and Wootton.