The reality star and her ex, who split this summer after nine years, have been spending time together and as a family with their three children Mason, 5, Penelope, 3 and Reign, 11 months.
“Kourtney has always been taking it one day at a time,” says a source close to the Keeping up with the Kardashians star, 36. “But when you’re with someone for that long and he’s the father of your kids, you want to do everything you can to make things right.”
For his part, Disick, 32, who checked into rehab in October and is still undergoing counseling, is focused on his family – and his sobriety – says a source.
“Scott knows he has to focus and work hard every day to keep his promise to his family,” says the insider. “He wants to be a family with Kourtney and the kids.”
RELATED VIDEO: Kourtney Kardashian and Scott Disick Spend Quality Family Time
And Kardashian, whose famous family invited Disick to their Thanksgiving dinner, is cautiously optimistic about her ex’s progress.
“She is starting to trust Scott more,” says the insider. “She is happy that he is finally taking care of himself.”
• Reporting by PERNILLA CEDENHEIM and ELIZABETH LEONARD
For more on Kourtney Kardashian and Scott Disick’s relationship status, pick up this week’s issue of PEOPLE, on newsstands Friday