There were two Joseph Brewers in Reynolds county, Missouri in the 1900 census.
Joseph A. Brewer was married to Caroline.
They have Belle (though she is not listed in the census as she is already married, and living next door), and they have 5 sons: King (born 1882) Willie Born 1888 George D. (married Myrtle) born 1891 Guy born 1893 Harry born 1897
My grandmother has some memories of George and Myrtle and their sons. My great-uncle said that George was an inspector for Railroad accidents or something, like an investigator. My Grandmother remembers hearing Guy's name mentioned, and that Belle had a bunch of brothers.
The 1900 census lists Joseph and Carolina being married 22 years, which would have been about 1878. Belle was born in November of 1878. I don't know if Joseph Carolina had any children after the 1900 census, but by 1900 Caroline was 47, so probably not.
The 1900 census lists Carolina having 7 children, but 5 still living (and they had Belle. She was already married to Charles Edward Johnson and had her son Clarence by this time).
Thanks everyone for all your help. If you find anything else, keep it coming.