Still, she adds, “Carolyn’s suggestion was lovely that he call them. He was, by all accounts, a lovely, gracious person, but maybe that moment was too difficult for him to be able to reach out and say something to someone who’s just lost their parent in a very public and dramatic way.”

The new biography sheds new light on the private side of Carolyn, who died on July 16, 1999, when a plane, piloted by John and also carrying her and her sister, Lauren, crashed into the waters off of Martha’s Vineyard.

“The press attention really terrified her,” says Beller. “There was a vulnerability. And I think somehow the press attention and scrutiny just touched a nerve and it stole a lot of her joy.”

The author hopes her book will remind people of Carolyn’s warmth and empathy.

“She had a lot of compassion,” says Beller, “and she was very caring and a good friend.”

Carolyn Bessette-Kennedy once urged her husband, John F. Kennedy Jr., to extend support to Prince William and Prince Harry following the death of their mother, Princess Diana, in 1997.

According to a new biography, Once Upon a Time: The Captivating Life of Carolyn Bessette-Kennedy by Elizabeth Beller, excerpted in this week’s issue of PEOPLE, Diana’s death after a high-speed chase by photographers in Paris unnerved Carolyn. She had struggled with the relentless paparazzi outside their Tribeca apartment.

After Diana’s death, Beller writes that “Carolyn tried to get John to call Princes William and Harry to give his condolences when it came out that Diana had hoped for her sons to emulate John’s modesty in the face of media obsession.”

John was reluctant, Beller continues, “as he didn’t know them and thought that their situations greatly differed.”

“He had met [Princess Diana] once or twice,” Beller writes. “And the fact that she had died while being chased down by paparazzi, he was aware of the fact that their [he and Carolyn’s] lives were becoming overwrought with attention and he was upset.”