You can obtain a copy of the death certificates for Joseph and Emma, which should show the names and birth locations of their respective set of parents.
The following looks like it might be your Joseph.Combined info from TX Dth Idx Online 1964-1998, and SSDI (Soc Sec Dth Idx):
Joseph E. Brandin, b 22 Jul 1887; d 15 Nov 1979 Tyler Co, TX; last residence Woodville, Tyler Co, TX; SS card issued in TX; single [single can also mean widowed, divorced or separated, since I couldn't find Emma, I assume he was widowed - she may have died too early for either index]
If you go to the TX Dth Idx Online and type surname of Brandin and county of Tyler you will find several, probably either brothers, or cousins. http://vitals.rootsweb.com/tx/death/search.cgihttp://vitals.rootsweb.com/tx/death/search.cgi
George Herman b 1916 Wilfred Sevran b Jan 1919 Joseph Benjamin b Nov 1919 Howard G. b 1925
Using an online directory http://www.four11.comhttp://www.four11.com -- type in surname of Brandin, state of TX and among the list you will see five in Woodville.If it were me, I'd get in touch with these people.
Check Tyler Co, TX GenWeb site, some GenWeb counties are putting their cemeteries online.You may find other family members buried there, too.And, if the above Joseph is yours, Emma is probably buried next to him.Post a query on that site, Brandin probably isn't too common, and someone may recognize the family.
You say you can't find anything, be sure to talk to family members, beginning with the older ones, but don't forget cousins, too.You neve know who heard the old family stories, and then who remembered them.Have you been in touch with your aunt Shirley or any of her children?