If Willie Joe had a brother named Johnnie, the parents appear to be Robert L Glasscock and Lorene Wheat. (Also, I found Johnnie's obituary.)
"Texas Birth Certificates, 1903-1935," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:VXGV-13N : 4 December 2014), Willie Joe Glasscock, 04 Mar 1935; citing , Smith, Texas, United States, certificate 26025, Bureau of Vital Statistics. State Registrar Office, Austin; FHL microfilm 2,283,842.
Lorene was the daughter of John F. and Sarah Wheat.