​Frank Sinatra at 100

That kind of attention was a constant in Sinatra's life. When bobbysoxers swooned for "Young Blue Eyes," they were swooning for a married man. He'd married the former Nancy Barbato in 1939; she gave him three kids.

But his private life was about to collide with his sweet-faced public persona. He'd leave Nancy in 1950 for screen siren Ava Gardner.

Nancy Sinatra on Frank Sinatra's marriage to ... 02:10

"She was fantastic," said Nancy Sinatra. "I met her when I was, what, 11? And I could see it. She was on the fast track, and he wanted to be on the fast track. And he usually got what he went after."

Still, Sinatra and his first wife -- who is now 97 -- remained tight.

"My mom had one great love of her life, and that was my dad," said Nancy.

Rocca said, "She knew him before he was a superstar."

"And to this day she still loves and adores him," said Nancy. "I asked him once, if he had it to do again would he leave mom for Ava? And he said, 'No.'"

Sinatra was already in a big slump when his marriage to Gardner flamed out after two tempestuous years, leaving him devastated.

"I think he hit rock bottom pretty much at that period," said Nancy. "It was tough."

But Sinatra was about to pull off the greatest second act in showbiz history, with a major assist from Ava Gardner.

"She was a huge help to him, because she was an influence in getting the Maggio role in 'From Here to Eternity,'" said Nancy.

Gardner was pals with Columbia Pictures president Harry Cohn. "She even said to him, 'You know who should play Maggio, don't you? That son-of-a-bitch ex-husband of mine!'"

His famous death scene breathed new life into Sinatra's career. He earned an Oscar, then signed a one-year deal with a new label: Capitol Records.

In Capitol's Studio A, the man and his music merged. At the height of his powers, Sinatra channeled the agony of lost love as no one else could -- and you could hear it in his voice.

As his bandleader and arranger Nelson Riddle put it, "Ava taught him how to sing a torch song. She taught him the hard way."

Frank Sinatra Jr. had a front-row seat. For a time, he was his father's musical director.

"I think the magic word was truth," he said. "The common denominator under every equation was truth."

Frank Sinatra Jr. with Mo Rocca at Capitol Records' Studio A. CBS News

"When you were conducting with him, would you see him sort of really go deep into the song?" asked Rocca.

"Absolutely," said Frank Jr. "When Bing Crosby sang, you believed him. When Sinatra sang, you believed him. This is really the thing."

As the guy who knew how to swing -- and might very well take a swing at you -- Sinatra defined the limits of cool, on stage and off.

How big a tipper was he? Huge, said Nancy: "One parking guy, I think he gave him $200, and the guy said, 'Well, thank you, Mr. Sinatra, that's the biggest tip I've ever had in my life. The other biggest tip was $100.' He said, 'What cheapskate gave you that?' He said, 'You did, Mr. Sinatra.'"

He was generous in other ways as well: Sinatra was, by all accounts, a great friend to politicians. He organized JFK's pre-Inaugural gala. And he was close to fellow performers, like "Rat Pack" members Dean Martin and Sammy Davis Jr.