Kate Middleton and Meghan Markle may have been two outsiders brought into the royal family, but that didn’t create an instant bond, author Omid Scobie writes in his new book Endgame.

In the book, published Tuesday and originally excerpted in PEOPLE, Scobie writes that Kate and Meghan had little in common,

but the rift between Prince Harry and Prince William didn’t help in the early days of their relationship.

Meghan and Prince Harry got engaged in November 2017 and wed the following May. During that time, Kate and Prince William juggled royal duty with parenthood to two young children — Prince George,

now 10, and Princess Charlotte, now 8. Kate also gave birth to Prince Louis, now 5, three weeks before Prince Harry and Meghan’s royal wedding.

“Still, for Meghan, who found much of her time as a working royal a lonely and isolated experience,

there was a hope that Kate would be someone she could at least turn to for an encouraging word during her lowest points,” Scobie writes in Endgame, which chronicles both the breakdown of the royal family and the weakening of the modern monarchy.

“They were once both outsiders, middle-class women brought into the house of Windsor for unimaginably different lives. Kate, however, was uninterested in forming this kind of bond with Meghan,” he writes.

Scobie, who has covered the royal family for more than a decade, writes in Endgame that a source said Kate “can be cold” if she does not like someone and “wasn’t a fan” of Meghan.

“She spent more time talking about Meghan than talking to her,” another source said, Scobie writes.

On recent occasions, Scobie claims in Endgame that Kate has “jokingly shivered” when her sister-in-law’s name is mentioned. While Kate and Harry, 39, previously shared a positive bond, Scobie says that relationship is also in the rearview.

Quoting a source who knows the family, Scobie writes in Endgame, “She was closet to Harry, and she will always look back fondling on those moments…and the relationship he had with their children…but to her, there is no way she could ever trust them after all their interviews.”

The Duke and Duchess of Sussex’s step back from royal life and U.S. move in 2020 also put more strain on William and Kate to “fill the working void left behind,” Scobie writes.

In Harry & Meghan, the Netflix series chronicling the couple’s love story and current chapter released last year, Meghan spoke about learning about the surprising realities of royal life during an interaction with Kate and William.

Meghan said in an interview on the show, “When Will and Kate came over and I had met her for the first time, they came over for dinner. I remember I was in ripped jeans and barefoot. Like I was a hugger, always been a hugger. I didn’t realize that that is really jarring for a lot of Brits.”

“I guess I’d start to understand very quickly that the formality on the outside carried through on the inside,” she continued, referring to the etiquette rules followed by the royal family, which she believed were only observed in public.

“There is a forward-facing way of being and then you close the door and you relax now,” Meghan said. “But that formality carries over on both sides. And that was surprising to me.”

Prince Harry also looked back at the same dinner in his memoir Spare, published in January. The Duke of Sussex said that it happened before he proposed in November 2017, and Meghan prepared the home-cooked meal.

“We talked about Wimbledon that night, and Suits, and Willy and Kate weren’t brave enough to admit to being superfans. Which was sweet,” Harry wrote in Spare, referring to the legal drama Meghan starred in for seven seasons. Earlier in the text, Harry wrote that his brother and sister-in-law were “religious” viewers of the show and were shocked to learn he was dating Meghan, who played paralegal Rachel Zane.

Recapping the dinner, Harry continued, “The only possible discordant note I could think of was the marked difference in how the two women dressed, which both of them seemed to notice. Meg: ripped jeans, barefoot. Kate: done up to the nines. No big deal, I thought.”

Recently speaking to PEOPLE about Endgame, Scobie said that Meghan has “moved on” from the royals, but things are different for Harry.

“Quite early on in the [book-writing] process, some of those Meghan sources that I really leant on in the earlier years this time were like, ‘You know what? She doesn’t want anything to do with it,’ ” Scobie told PEOPLE in last week’s exclusive cover story.

“For Harry, it’s different. He still has unfinished business when it comes to his battles with the press. His challenge will be to find something that balances that out so we can see him working in a space that isn’t connected to the ties that bind from the past,” Scobie says.

The Duke and Duchess of Sussex are resetting for their next chapter.

“What we’re seeing — and will see more of I think — is Heghan 2.0. Part Deux. They know of their supposed failures and how it’s viewed, but they have almost gone more tech than Hollywood. Fail big and all that,” a source tells PEOPLE. “They have swapped in and out all sorts of projects and people and are embarking on a total system reboot.”

“They have a constitutional inability to look in the rearview — why should they? They are all about the future,” the source adds.

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Source: USA Today