1880 Polk Co Ark has Ida and John H living with father and mother Wm L. and Nancy L Kilgore. Their evidently left Ark for Tx before returning to Cleveland Co by 1880. The 3 oldest kids were born in Ark, Ida in Tx in 1873-78 depending on which age from censuses. This puts Wm Kilgore as 26 in 1860 that matches with William in 33rd Ark Inf at age 27 on enlistment. Looks pretty good match up to me. Couldn't find them on 1870 census to document as oldest dau should be there, being born in 1865.