Hello. If Charles H. Miller had a daughter in 1906 then it appears to have been an illicit birth or an adoption because in the 1910 census Julia and Charles are shown married for ten years and Julia is seen to have given birth to "0" children. I noticed that in the 1920 census there are now two children, Adeline and Alfred, both thirteen years of age.
By the way.. I have found the obituaries of this Julia W. Miller's parents, they contain a wealth of family information. I can post the obits here If you care to see them.
Also found the news items concerning the 1928 divorce of George Stone Cary from Margaret Boyce, by 1930 they were both remarried.