There actually is a wife listed in the 1880 census-Delia,age 21,born in TX.
Then it looks to me like the family moved to Indian Territory,OK? 1900 census,Elmore-Chickasaw Indian Territory,OK McAdams,Nathan-born Mar 1851;49;married 25yrs;born TX wife-Delia-born Jan 1858;42;10 children born, 7 living;born TX dau.-Mary-born Feb.1884;16;born TX dau.-Maggie-born Nov.1886;13;born TX son-Frank-born June 1893;6;born TX dau.-Pearl-born July 1895;4;born TX
The next farm over is John H.McAdams age 22-born Oct 1877;married for 3 yrs. to Ella-age 24,and her daughter,who is 8; can not clearly read her name, but her surname looks like "Custer".
The next farm over is Jeff McAdams,age 20,born Aug 1879,married for 3 yrs to Janie-age 20,born Mar.1880.
The parents I could not locate after that-probably somewhere horribly misspelled; but the boys John and Jeff are in various places around OK in later years. There is a William McAdams next door to Jeff in 1910, but not with a spouse that you've named, so do not know if he is of this family or no.