If General Jackson was really an uncle, the family name would be Arnold. Jonathan and Julia Neale Jackson had four children, Thomas J. Jackson being the third. Jonathan and six-year old Elizabeth died of typhoid fever in March 1826, Julia Jackson giving birth to a daughter named Laura Ann the day after her husband died. Jackson's only brother Warren died at age twenty, so the only male descendants (nephews) being children of Laura Ann Jackson. She married Jonathan Arnold on Sept. 1, 1844.
http://www.vmi.edu/archives2.aspx?id=5113

This may help with other Jacksons in the family line --
http://www.vmi.edu/archives2.aspx?id=5005