I tried looking for the family on the 1910 census in NE, when Carl would be 3 yrs old,but the only male head of household in Madison Co, NE born in Sweden is Otto A., and I thought maybe the "A" was for August.But, he is already a widower and no sign of young children in the household.His mother-in-law is Johnson.
1910 census Madison Co, NE:
Wilson, Otto A., hd, 52 Wid, b Swed, Swed, Swed
" Amma, dau, 26, sgl, b IA, Swed, Swed
Johnson, Mary, m-in-l, 82, wid, 9 ch, 3 lvg, b Swd, Swd, Swd
Otto arrived this country 1877 and is naturalized, speaks English.Mary arrived this country 1883, speaks Swedish.
Well, I guess that isn't your man.1900 census Platte Co, NE:
Wilson, Otto A., 42 wid, b Swed
" Emma, 16, b Ia
Johnson, Mary, 72, wid, b Swed
But, is this your Carl?1920 census Garfield Co, NE (Burwell is in Garfield Co, NE)
Ballard, Harry B., hd, 32, Md, b NE, OH, IL
" Bonnie, wf, 26, Md, b NE, unk, unk
" Hilah V., dau, ? 11/12, b NE
Wilson, Carl, hired hand, 12, b NE, unk, unk
Handwriting not real clear, some of the names are hard to read.But Carl Wilson is very clear.Looks like it says he is a hired hand, choreboy on farm.
You might look for guardianship records on the minor Carl.If his father owned any land, the courts would appoint a guardian to report back to the court of any sale of the estate, to protect the interest of minor children.