Barker, 45, proposed to Kardashian, 42, on Sunday at the Rosewood Miramar Beach Hotel in Montecito, Calif. She announced the news on Instagram, sharing photos from the romantic moment with the caption: "Forever @travisbarker."
Following the news of the engagement, Disick is distancing himself from his ex's famous family in order to "make his peace" with the engagement news, according to the source.
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"Scott hasn't really wanted to deal with Travis and Kourtney because he didn't feel like he'd have to," the source says. "At first, it seemed like it was just a casual relationship to him, nothing serious. So he pretty much put that on mute. Hasn't been giving it too much brainpower, thinking that eventually, they'd break up."
Presley Ann/Getty; Dimitrios Kambouris/Getty
The source continues, "But that didn't happen and now he's being forced to deal with it, which is uncomfortable. He knows he has to lean into the discomfort and get past it. He understands that it's not Kourtney's job or Travis's job to make him okay with this. It's his job, and if he's going to co-parent with Kourtney, which he has been, he has to process this and make his peace with it."
The source says "distancing himself from the family" is a way for Disick to achieve that. "It's not about them, it's not about Kourtney. It's about him needing some time to process this and deal with it on his own, without them. He'll come around soon."
Another source told PEOPLE earlier this week that Disick is "not happy about the engagement."
"Scott never approved of Kourtney dating Travis. He has struggled with their relationship," the source said. "He always had this idea that he and Kourtney would eventually get back together. He was pretty shocked when he found out that she was dating Travis."
Getty Travis Barker and Kourtney Kardashian
PEOPLE broke the news of Kardashian and Barker's relationship in January. As their romance progressed, a source said Disick was "struggling" with how serious the pair were becoming.
During the two-part Keeping Up with the Kardashians reunion in June, Disick gave the Poosh founder his blessing to move on with other people: "I think if you really love somebody, you want them to be happy no matter what. So I do give her a blessing to be happy," he told host Andy Cohen at the time.
"Yo is this chick ok!???? Broooo like what is this," Disick allegedly wrote to Bendjima, sharing a photo of Kardashian and Barker kissing. "In the middle of Italy."
Bendjima, 28, allegedly responded, "Doesn't matter to me as long as she's happy. P.S. I ain't your bro."