Past Loves & Secret Disguises: The Biggest Bombshells from a Colorful New Jackie Kennedy Biography (Exclusive)

There was always more to Jacqueline Kennedy Onassis than the life she led in public. According to a new biography — Jackie: Public, Private, Secret by J. Randy Taraborrelli — exclusively excerpted in this week's issue of PEOPLE, there is still much more to her discover.

In the book, Taraborrelli shares new details of Jackie's private life, including her relationship with former lover, architect Jack Warnecke, and how she really felt about a brief dalliance between her son, John F. Kennedy Jr., and Madonna.

Below, Taraborrelli discusses some of the biggest bombshells from the book.

Jackie's Mom Initially Wanted JFK to Marry Her Younger Daughter, Lee

While it was Jackie who would go on to marry John F. Kennedy in 1953, her mom, Janet Bouvier, initially thought that her younger daughter, Lee, might be a better fit for the future president.

John was a young senator from Massachusetts, and Jacqueline Bouvier a "camera girl" and reporter for the Washington Times-Herald, when she — and her sister, Lee — met JFK at a party at the Kennedy's Palm Beach estate.

"JFK and Lee actually got along better than Jackie and JFK," Taraborrelli tells PEOPLE. "And Janet felt that Jackie [who was four years older than Lee] needed to get settled. Lee did not need to get settled yet."

In the end, Jackie's marriage to JFK was a decision not entirely based on a love connection, but as Taraborrelli puts it, on "Which one needed to get settled?"

"And when you think about it, it's mind-blowing that in that moment, Janet decided it was going
to be Jackie. And that decision changed everything for those two girls," he says.

JFK and Jackie announced their engagement on June 24, 1953, and tied the knot at St. Mary's Church in Newport, Rhode Island, in September 1953.

Jackie's Second Husband Was at the White House the Night of JFK's Funeral

While it's been previously reported that on the night of JFK's funeral, Aristotle Onassis spent the night at the White House, Taraborrelli writes that the shipping tycoon also visited Jackie in her private quarters that evening.

At the time, Onassis was dating Jackie's sister, Lee. But according to Taraborrelli, after the assassination, "he called Jackie and said that he was in town for the funeral and was staying at a hotel. And she felt like she had no choice but to invite him to the White House."

Ultimately, Onassis stayed in the spartan living quarters of a White House staff member — a detail which left Lee allegedly "mortified," Says Taraborrelli: "She felt like Ari was going to be very upset. But Onassis was the kind of guy who could really make the best of most any situation."

Onassis didn't attend the funeral. Instead, he stayed at an empty White House, where even the phone operators had left to attend the service.

That evening, after the service, Taraborrelli writes that according to two sources, Onassis was "seen knocking on Jackie's door." But, he left the room within the hour, and, says Taraborrelli, "I can't imagine the grief Jackie was going through. I don't think anything happened between them at that moment."

Jackie Dated a Greek Film Director After Her Second Husband's Death

Jackie tied the knot for a second time with Greek shipping magnate Aristotle Onassis in Oct. 1968, a marriage that ended when Onassis died in March 1975 of respiratory failure.

After his death, Jackie dated Greek film director Michael Cacoyannis, a short-lived romance that ended when the Zorba the Greek director said he wanted her to stop working.

Initially, Cacoyannis had become friendly with Onassis, though the two suffered a falling out until Jackie attempted to mend their relationship.

"When Onassis was on his deathbed, Jackie wanted Michael and Ari to have a reconciliation," Taraborrelli says. "So she asked Michael to go to Onassis, to his deathbed, and reconcile with him. And they did."

After Onassis died, Jackie moved to New York and got a call from Cacoyannis, asking, "What if
you and I get together?"

"According to the people that we talked to, she had a leaning toward Michael, because he reminded her of Onassis," Taraborrelli says. "He was Greek, he had the same sensibility; she missed Onassis ... so they ended up having an affair."

Then Jackie got an offer to work at the publishing house Viking Press, where she would make $200 per week. Michael — shocked that she would take a meager offer when she had inherited millions from Onassis — told her, "Greek women don't work, and I don't want you to work. ... You have to choose between this job and me."

According to Taraborrelli, Jackie confided in Onassis' sister Artemis, that the choice, for her, was easy. "When a man makes you choose between him and something else and you choose him, you're in trouble," she said.

Jackie Attended One of Madonna's Plays (in Disguise) During John F. Kennedy Jr.'s Brief Fling with the Pop Star

As Taraborrelli details, Jackie was not happy to discover that her son was having a fling with pop megastar Madonna in the 1980s. And while it's been rumored that Jackie's main issue with the pop star was her resemblance to Marilyn Monroe (a rumored paramour of her late husband's), the real issue was much less superficial.

"[Jackie's] problem with [Madonna] was that she was married," Taraborrelli tells PEOPLE, adding that Jackie was also "confounded by Madonna's penchant for attention. Jackie had spent her entire celebrity life avoiding paparazzi, whereas Madonna would court paparazzi. And Jackie just couldn't understand any of that."

Despite his mother's reservations, JFK Jr. at one point asked his mom to attend one of Madonna's plays — and she complied, albeit, in disguise.

"I interviewed somebody who worked with Jackie at Doubleday, who said that she went with Jackie to the show; that Jackie wore a red wig so that she wouldn't be recognized," Taraborrelli says. "She put the wig on, and she asked this woman, 'How do I look?' And the woman said, 'You look just like Jackie Onassis in a red wig.'"

According to the author, Jackie drew the line, however, at meeting the musician backstage: "She thought Madonna was good in the show. But she also felt like she didn't want to validate the relationship that John had with Madonna by being photographed."

Jackie Had a Loving — and Years-Long — Relationship with Architect John Warnecke

While it has been written that Jackie began dating architect Jack Warnecke, whom she had hired to design her late husband's eternal flame memorial at Arlington National Cemetery, in 1964, many aren't aware that the two shared such a deep connection.

"They were together for four years and they were really very important to each other," says Taraborrelli. "And she really did love him, and he really was crazy about her."

Warnecke shared some of his memories with Taraborrelli in a 1998 interview, but with one caveat. Out of loyalty to the famously private Jackie, Warnecke asked that everything remain under wraps until a decade after his death. He died in 2010, when he was 91.

As Taraborrelli writes in his book, the architect planned to propose to Jackie during a 1966 trip to Hawaii, but the couple broke it off when Warnecke admitted that he was deep in debt.

Still, the two remained close. Years later, in the final months of her life, Jackie would receive a Valentine’s note from her former lover. The note lead to a reunion at her apartment several months before her death on May 19, 1994, from non-Hodgkin lymphoma at age 64.

From the book: "In [our] 1998 interview, Jack said, 'As I took my seat, Jackie handed me a stack of envelopes neatly tied together with yarn. My presence that evening was part of a ritual. Every night that week, she was inviting a trusted friend or family member to her home to take part in it.

"Jackie untied the yarn and took a letter from the stack. She read it before placing it into the fire. He recalled, 'There were letters from Jackie’s children, John and Caroline ... There were also letters from Jack Kennedy, Aristotle Onassis, her father, Jack Bouvier and even a few from me.' She held one of the photographs and stared at it. It was her and Jack [Kennedy] on the day of his inauguration. 'Keep this for me, will you?' she asked."

According to Warnecke's daughter, Margo Warnecke, there's still more to discover. "My father left behind an unpublished memoir: Camelot's Architect,: Life, Modern Architecture and the Kennedy's," she notes. "It's part memoir, part love story. The memoir charts his life from his first encounter with JFK as a senator in 1956, to helping him preserve and redesign Lafayette Square, to the magical social scene and being an intimate of the president and his court, to JFK's assassination and designing his grave, to his long romantic relationship with Jackie and all the excitement, intrigue and personalities in-between."