Before relating info from the 1860 census, I'll ask if you have been to the Find-A-Grave site? There are two listings for George Washington Nichols Sr. He died April 15, 1900, but there is a controversy as to his actual burial site. There are very informative write-ups with each listing.
The 1860 census lists: George Nichols, 39 TN; Martha 30 VA; Sarah 11 TN; Lutitia 9 TN; twins George (Jr?) and Mary 7 AR; James 3 AR; and Mariah 2 AR.
1870 lists the name as Nicholds. Sarah may have already married and moved from the family. Lutitia has married John McCombs (name a bit unclear) and lives close to her parents. Other children from 1860 are still at home with additional children: William 6; Perry Lee 4 and Margaret 2.
George may have had a brother named Thomas also living close by.