I believe I have located the family James Wright on the 1850 Census. This census would put James, Hamilton and George in the same household.

1850 Federal Census- Washington, division 3 date: 15 Nov 1850
John Wright,w/m,46,S.Carolina
Sarah Wright, w/f. 42, S.Carolina
Hamilton Wright, w/m,20,Georgia
James Wright, w/m,16,Georgia
Nancy Wright, w/f,14,Georgia
Geo? Wright, w/?,9,Georgia
William Wright,w/m,7 Alabama