I suspect the person you should be looking for is a George Dorsch rather than Charles.
The 1910 census lists an Elizabeth Dorsch 77 living two houses from John and Elizabeth Gebauer in Pittsburgh. Living with her is her son Charles 56.
The 1860 census lists a Charles Dorsh 5, Elizabeth 7, Elizabeth 28 with George 33 in Pittsburgh. Elizabeth and George were born in Darmstadt, Germany.
Finding either the Gebauer or Drosch Families in the census in the Pittsburgh census is not easy. The only other census I could find that was of any help was for John and Elizabeth in the 1900 census. They are misindexed under the spelling of Leabur living in McKeesport (it should be Geabur).
Check with the Historical Society of Western Pennsylvania or the Western Pennsylvania Historical Society to see if they can help. Perhaps by tracking down the other children of George and Elizabeth you can find the info you need.
If you haven't already I suggest getting Elizabeth Gebauer's death certificate and obituary. The latter may list siblings.