I wondered if perhaps Nancy was the mother and remarried after her husband died or left.Unfortunately the 1870 census does not give relationship to the head of the household as later censuses do.I went back to 1860 and found the following:
This is the only IN 1860 entry for Posey or Gibson county that matched.
I searched an Indiana marriage index and found:
David Smily married Nancy Overton02 Jul 1857 Posey County
Unfortunately I was unable to find a marriage of a Nancy Smily to a Peyton Schusler, which would have confirmed the theory.I was also unable to find Thomas or John in later census records, though if they were not the head of the household they wouldn't be in the index for 1900 or 1910.I did find a William Smiley that is possibly the brother to Sarah:
1900/IN/Vanderburg/Evansville/ED100/p.289A Smiley, William/head/w/m/Sep1859/40/marr1yr/IN IN IN/day laborer Smiley, Augusta S/wife/Jul1869/30/marr1yr/4ch-3liv/IN GER GER Smiley, Esco/son/Sep1890/9/s/IN IN IN Smiley, Desie/dau/Jul1894/5/s/IN IN IN MIller, Lillian/stepdau/Mar1890/10/s/IN IN IN Miller, Bessie/stepdau/Aug1892/7/s/IN IN IN Miller, Walter/stepson/Feb1895/5/IN IN IN
It appears the first two children belong to William, the Miller children belong to Augusta.I believe they also had a child together named Carl in 1901, who died in Evansville in 1972, according to the Browning Funeral home site.In 1910 William has moved back to Gibson County and is farming and is still living in 1930.