The 1910 US Census for Justice Precinct 5, Houston, shows J. R. Beeson living with wife Mattie. This is the second marriage for both, and they have been married for 7 years. Mattie has had 6 children, 5 of whom are living. The children living with them are: Cha. Beeson, 12; William Travis Beeson, 10; gladys Beeson, 6; Hamilton Beeson, 4; Carmel Beeson, 2; AND daughters Lucretia Collins, 17; and Lillie Collins, 12.("United States Census, 1910," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/MK1P-XQ5 : accessed 21 March 2015), J R Beeson, Justice Precinct 5, Houston, Texas, United States; citing enumeration district (ED) 73, sheet 7B, family 133, NARA microfilm publication T624 (Washington, D.C.: National Archives and Records Administration, n.d.); FHL microfilm 1,375,578.)
The 1920 US Census for Grapeland shows James R. and Mattie living with children Gladys, Hamilton, Freddie, Woodrow and Vora.("United States Census, 1920," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/MCSQ-L8S : accessed 21 March 2015), James R Beeson, Grapeland, Houston, Texas, United States; citing sheet 6B, family 113, NARA microfilm publication T625 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 1,821,819.)
The death record for Gladys Smith shows that she was born on 06 Aug 1903, the daughter of Jim Beeson and Mattie Brown.("Texas, Deaths, 1890-1976," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/K38V-77N : accessed 21 March 2015), Jim Beeson in entry for Gladys Smith, 13 Nov 1975; citing certificate number 82554, State Registrar Office, Austin; FHL microfilm 2,243,834.)
The death record for Woodrow Wilson Beeson shows that he was born on 25 Sep 1912 to Jim Richard Beeson and Mattie Brown.("Texas, Deaths, 1890-1976," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/K38R-NQN : accessed 21 March 2015), Jim Richard Beeson in entry for Woodrow Wilson Beeson, 12 Feb 1976; citing certificate number 15155, State Registrar Office, Austin; FHL microfilm 2,243,928.}
Given that children on both sides of Hamilton had Mattie as their mother, and given the 1910 Census which shows 5 children for her, 3 Beeson children and 2 Collins children, I think it is certain that Mattie Brown Collins Beeson is Hamilton's mother..
The way to confirm this would be to get a copy of Hamilton's 24 Jan 1976 San Diego County, California Death Certificate.(State of California. California Death Index, 1940-1997. Sacramento, CA, USA: State of California Department of Health Services, Center for Health Statistics. Ancestry.com. California, Death Index, 1940-1997 [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2000.)