Found some documentation to support some of your information.
Charles L Hollingsworth married Viola May Eddleman Aug. 24, 1899 in Knox, Ind.
Found 3 documented births (Knox, Ind.) for Charles & Viola 1) born July 15, 1900 - this is Muriel D.(confirmed by SSDI) 2) born Sept 20, 1901-male - possibly James 3) born Sept 6, 1905 - this is Roy/Royal
Upper Indiana Cem. Knox Co. Charles Lindley Hollingsworth b. 4/21/1877 d. 2/6/1906 Headstone says "brother"
Royal Lindley Hollingsworth b. 9/5/1905 d. 12/23/1938 Same cemetery as Viola's parents
1900 Vincennes, Knox, IN Hollingsworth, Lindly b. Apr 77 Ola b. Aug 82 married <1yr no children
Haven't found Viola in 1910
1920 Union, Vanderburgh, IN Rettig, William O 49 Div. KY Elizabeth 16 KY Roy Frank 14 IL Hollingsworth, Viola 37 Wid. IN Housekeeper Hollingsworth, George 8 IN Boarder
Clearly George was not Charles' son as he had been dead long before the birth. I've found no record of the birth yet.
Chicago Cook, IL deaths- Harry W. Fulford d 6/28/1937 Chicago father-Willard mother-Marie Antoinette Paniel spouse-Muriel D.
Here are a couple of possibilities for the 2 possible mystery boys (James & Charlie)
1910 Washington, Knox, IN Eddleman, Joseph H. 31 IN Minnie 30 IN Selma 10 IN Mora 7 IN Hollingsworth, James 8 IN Nephew Dove, Fred 24 IN hired hand
1910 Washington, Knox, IN Patrick, James 59 Clerrsa 50 Basil 27 Bertha 18 W. Edwin 24 Hoffingsworth, Charlie 6 no relation
Viola Rettig died Mar 7, 1964 or thereabouts.You might contact the Vincennes Public Library as they often have old newspapers in the stacks or on microfilm.Sometimes a reference librarian will look up an obit.Muriel should have provided the information, & I would assume she knew about her brothers.