Birth records for some of the other children in the 1920 census family (Alma L, Nettie E) listed above show the same mother's maiden name, Patton, indicating that this is, indeed, the correct family.
The 1910 census shows older daughters Edna, b. c. 1902, Sarah, b. c. 1903 and Alma, c. 1907.
Children in the California birth index born to a father named Fellows and a mother named Patton (all in Los Angeles County) include
Sarah I, b. 6 Aug 1905
Ida M, b 15 May 1909
Amelia A, 1 Aug 1910
Nettie E, 31 May 1912
unnamed female, 6 Sept 1914
Louis, 10 Feb 1916
Maurice A, 31 Oct 1917
Note that the California birth index shows the child born on Aug 1, 1910 as being named Amelia A, not Hester. Perhaps she is Hester Amelia?
Hester's husband Frank Toon Conklin died 16 July 1960 and is buried in Downey, CA, and is buried in Forest Lawn, Glendale, Plot: Section K, Lot 131, Space 10, in an unmarked grave.
A family tree on Ancestry indicates Sarah Idela Fellows is the sister of Hester. Sarah married 1) Terry Heaton who died in 1931 and 2) Lawrence Leroy Turney. They had children Ruth Lorraine Turney (married Donald Andeen Olson, who died in 1984), 18 Feb 1934 to 30 Nov 1996 and Clara Patricia Turney, 31 Mar 1936 to 8 July 1992 (married Guy Dilley, who died in 2006). Both of these nieces of Hester died in Sacramento County.
Ruth and Donald Olson had Michael David Olson, died 15 Aug 1997 at the age of 46 in Citrus Heights, Sacramento County, California. He married Penny D Garcia and had with two children.
Info on Michael's widow, Penny D Olson of Citrus Heights, is available through some of the subscription services. She would be the widow (or possibly ex-wife) of Hester's great-nephew (her sister Sarah's grandson), and may have contact with other, closer family members.