(CBS News) In his new book, "After Camelot: A Personal History of the Kennedy Family, 1968 to the Present," biographer J. Randy Taraborrelli says there was a "certain lineage of succession" in the Kennedy family concerning the presidency.
"It was going to be JFK, it was going to be Bobby, it was going to be Teddy," Taraborrelli said. "And then it was going to be (Sargent Shriver), perhaps. He was never able to get there."
Shriver, who founded the Peace Corps. and was an ambassador, made important contributions, but was an in-law of the Kennedys. He married Eunice Kennedy in 1953. Taraborrelli said Shriver experienced a "glass-ceiling" to what he could achieve because of his association with the family.
"There's a quote from Sargent (in the book) where he said he just wished that there would be a point when people would be able to acknowledge him and recognize him for who he was and not for, you know, being a Kennedy in-law," Taraborrelli said.
Taraborrelli also contends Shriver didn't get the full support of the Kennedys when he ran as Sen. George McGovern's vice presidential candidate in 1972.
"There was always a sense it should have been -- should it be Teddy? When is Teddy going to run? When is it going to be Teddy's turn? So Sargent was always sort of fighting that."
Taraborelli has written bestsellers about Michael Jackson, Frank Sinatra, Marilyn Monroe, Madonna, Elizabeth Taylor, and others.
For more with Taraborelli on the Kennedys and his new book, watch the video in the player above.