::You mean someone else is following all these back-and-forths?  You have my sympathies ;-)  For the long version, I don't like "dating" (not usually used in  an extramarital context); I would use "extramarital relationship" (readers complain when we don't call a spade a spade on this) (but Ferrylodge is adamant on "courting").  Later, we need to indicate that McCain initiated the divorce and that she accepted it and that it was uncontested.  So, basing this on what's currently in Early life and military career of John McCain, how about (only the bold part new/different): 
 :::In April 1979,[57] while attending a military reception for senators in Hawaii, McCain met Cindy Lou Hensley, eighteen years his junior,[182] a teacher from Phoenix, Arizona who was the daughter of James Willis Hensley, a wealthy Anheuser-Busch beer distributor, and Marguerite "Smitty" Hensley.[176] An extramarital relationship began, and they traveled between Arizona and Washington to see each other.[183] John McCain recalls this starting after he and his wife Carol permanently separated[some source]; other sources put the separation later in 1979.[the three sources]  John McCain filed divorce papers in February 1980, which listed January of 1980 as the legal end of cohabitation[LAtimes].  She accepted at that time,[57] and the uncontested divorce became official in Fort Walton Beach, Florida, on April 2, 1980.[184] 
 ::As for the short version, I still don't like "dating", but it does have the advantage of being the coward's way out – duck the separation issue completely!  I could go for it, I think, but down the road a dozen editors will try to stick it back in.