Barbara, it appears that George M. Hammontree was indeed the father of John Henry Hammontree. It's a bit confusing, but here goes: 1870 Carmi, White County, Illinoispage 3246 July 1870 #559 #542 Hammontree, Miller55farm laborerb.p. TN Margaret 53 keeping houseTN William26TN ** George18IL Douthard 10IL [Garrett D.] Sarah9IL John7IL #561 #544 [2 houses away from the Hammontrees] Conner, Melvina55KY Mary20IL Thomas15IL James12IL David19IL
George M. Hammontree married Mary E. Conner 19 July 1872 in White County. Their son, John Henry Hammontree, was born ca 1872 per all available census [1880, 1900, 1920, 1930]. By 1880, Mary E. Conner Hammontree has either divorced George, or he has died. She remarried to William P. Jameson/Jamison on 26 February 1880 in White County, Illinois.
1880 White County, Illinois [LDS website] Carmi page 378D William Jamisonselfmarriedage 25 b. IL Father:IL M:IL MaryJamisonwifemarried32ILILKY HenryJamisonson6ILILIL ThomasConnorbrotherLaw single27ILILKY This is why you couldn't find John Henry Hammontree; he is with his mother and stepfather and is shown here as Henry Jamison!
You probably already have these: 1920 Clinton County, Missouri Lathrop ED 41 sheet 5B 1930 Clinton County, Missouri Lathrop ED 14 sheet? [didn't note this, but will show up in a search on Ancestry] 1900 Daviess County, Missouri Lincoln Twp. ED 55 sheet 6
1870 Illinois Hammontrees: Hammontree, Johnage 32 b. TN Hamilton Co. Mcleansboro p. 589 Hammontree, Lydia34TN Hamilton Co. Mcleansboro p. 539 Hammontree, Miller55TN White Co. Carmi p. 324 Hammontree, Wm.53TN Hamilton Co. Mcleansboro p. 592
See LDS Family Search under Miller Hammontree Also: WorldConnect at Ancestry under Miller Hammontree by Jerry N. Waddell [don't forget to check this, as it appears that Margaret is NOT George Hammontree's mother. His mother was a Martha]
For Conner origins: 1860 Carmi, White County, Illinoispage 537 #1566 #1556 Conner, John57 maleb. IN Lambert, Jane19 fem.IN Conner, Benjamin 20 maleIN Conner, Wily40 maleIN Conner, William19 maleIL Mary12 femaleIL David10 maleIL Thomas8 maleIL James6 maleIL
Above James through William, aged 19, appear to be your Conners. The ages match the 1870 census fairly well. Where is their mother, Melvina and their father? John Conner must be a relative of some sort, perhaps an uncle. Maybe by searching White County, you can find a bio or other record of them in Indiana.