I got curious about the Braniff captain story and found an NTSB incident report number: FTW79IA063. It's a short report which confirms the basics, that the captain suffered a heart attack.
You can find it with the at the NTSB query page with the incident number above or with N601BN in the registration field.
The story that the captain's wife was a member of the captain crew has been circulating online for over 10 years; there's a post on airliners dot net that refers to the incident report. There's a news article (Louisville KY Courier-Journal, 18 March 1979; via a wire service and apparently originally written for a Dallas paper) that seems to corroborate that part of the story; it has names of the the crew, responding physicians, etc. The actual page as it appeared in print is pay to read but below the image there's a link you can click to see the machine-read text. It's a little out of order and includes text from advertisements, but you can get the gist. If you search for "braniff stockstill 1979" the article should be high in the results.
Of moderate interest (IMO) from the article: "... [a situation] experts once predicted would occur three times a year on American air carriers[,] the death of a critical member of the flight crew. It was a prospect so grim that government agencies and the airlines constructed a series of safeguards that, through effectiveness or sheer luck, has prevented a commercial airline disaster as a result of crew death."
Apologies if this is too much topic drift. Also apologies for not including links; they were there but I had to remove them as I haven't posted before to give the software here a reason to think I'm not a spambot.