Marion did live a separate life, it wasn't just a stage name -- it was a very deliberately created character. I suggest you read John Waynes America" by Garry Wills http://www.amazon.com/John-Waynes-America-Garry-Wills/dp/0684838834 This was back when the studio system managed the "appearance" of actors -- and so also gay actors were shown "dating" female actors. It was all fake, even off stage.
John Wayne was a character who among other things, liked to ride horses. Marion didn't.
I've seen many, but not all of his movies, my favorite probably being The Quiet Man. I've read "John Wayne, American", I really enjoyed it. I would also recommend "John Wayne's America" by Garry Wills. He discussed in depth Wayne's stringent avoidance of military service in WW II among other topics.
I'm not sure what you consider a "decent" source, but there is an entire chapter in this book dedicated to the subject of Wayne's personal life and his on screen persona. I have no reason to believe it is any more or any less true than the previous titles mentioned.
From Greenwald's book:
"Wayne scornfully condemned films that he claimed deviated from wholesome American values. Yet in his own life, Wayne was not only married to three different women but engaged in multiple affairs with a whole array of Hollywood actresses and socialites. While he loudly denounced those whom he deemed to be morally impure, Wayne indulged an alcohol addiction and barbiturate and amphetamine habit for years." p.14
"Later in life, Wayne claimed he was unable to fight in the war because of his age, and the need to support his three children. Throughout World War II , he turned to a series of increasingly extreme measures to protect himself from being drafted. According to Garry Wills's 'John Wayne's America', the Duke did not even reply to letters from the Selective Service System and applied for numerous deferments" p.21
"During the Vietnam War, the draft-dodging Wayne vocally condemned teenagers who went to Europe or Canada in order to avoid the draft, calling them 'cowards', 'traitors', or 'Communists'." p.28
If you're worried about the sources for my sources, you should take it up with the authors.