Here is an obituary extract for your father, in case you have not looked at it recently.
"United States, GenealogyBank Obituaries, 1980-2014," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:QKG5-LSX5 : accessed 7 October 2019), Wayne Molaison in entry for Joseph "J A" Molaison, New Orleans, Louisiana, United States, 03 Apr 2011; from "Recent Newspaper Obituaries (1977 - Today)," database, GenealogyBank.com(http://www.genealogybank.com : 2014); citing Times-Picayune, The, born-digital text.
Two ideas for you to pursue: 1) Have you traced the other Molaison family members, to see if step- or adoption-relationships show up? 2) Are any of your cousins (Kovar or others) interested in genealogy? Maybe one could give you information, especially if that cousin is older than you and may remember more of the older relatives.
Genealogy is such a puzzle. I hope you find information that gives you peace. Good luck. -NGP