A source close to the reality star, 33, tells PEOPLE that she's "not looking to downsize or simplify" as she adjusts to her new life since announcing her split from Cutler after 10 years together earlier this month.
"She's trying to minimize the impact on her kids, so she'd love to bring them someplace really nice, really welcoming, really special where they can start putting down roots and make memories," the source says.
Cavallari and Cutler share sons Camden, 7, and Jaxon, 5, and daughter Saylor, 4.
After previously attempting to prevent Cavallari from purchasing her own house by withholding money as leverage in their custody battle, a second source told PEOPLE Monday that the NFL star, 37, finally agreed to release the funds.
Kristin is "definitely proceeding with house hunting and she is absolutely going to move into a new place, no question," says the first insider. "If there was one thing that was going to make Kristin roll up her sleeves and fight, it's her kids. This isn't about getting all of Jay's money or getting some big mansion or revenge.
Kristina Bumphrey/Starpix/Shutterstock; Jason LaVeris/Getty Kristin Cavallari, Jay Cutler
"It's always been about what's going to be best for her kids, what sort of home she wants them to grow up in, what sort of behavior she wants them to see modeled, what sort of men she wants her boys to become and what sort of woman she wants to be for her daughter," the source adds.
The second source also confirmed to PEOPLE that the exes have come to a temporary agreement on how to split time with their children.
According to court documents obtained by PEOPLE, the kids will remain at their current Nashville, Tennessee home, with Cavallari and Cutler switching off every other week to stay with their children.
Once the Laguna Beach alumna moves into her new residence, the kids will go back and forth between each of their parents' homes, with Cavallari hoping to close on her new home within the month."
In Cavallari's divorce filing, the reality star confirms she and Cutler — who tied the knot in 2013 — have had issues for the "last several years." According to the documents, Cavallari began looking for a new home as early as November 2019, and she says Cutler did not object to her doing so. In March, she says they "realized the attempt to reconcile was not working and knew a divorce was inevitable."
Once they returned home from their family trip to the Bahamas and were social-distancing together in home outside of Nashville, Cavallari says she told Cutler she had found new house for herself and their kids. According to the filing, "The settlement negotiations were not going well, and she decided she would need to move out." But she claims Cutler refused to release the money from their joint account as leverage in their custody battle.
Cavallari says Cutler told her "his attorney was going to tell their business manager to not release the funds," which she claims is Cutler's idea of "punishing her for not accepting his offer" of a settlement, according to the filing.
Cavallari insists she "has the necessary resources" to buy the property in Franklin, Tennessee, "in cash" and signed a contract for the home on April 27. But the next day, according to the filing, Cutler "attempted to intimidate" her "into accepting his parenting plan," telling her he would block her access to the money and refusing move out of their current house unless she agreed to his requests.
Broadimage/Shutterstock Jay Cutler and Kristin Cavallari
The new documents also confirm that the two are currently swapping time at home with the kids, three days at a time.
When he filed for divorce, Cutler cited "irreconcilable differences," while Cavallari cited both "irreconcilable differences" and "inappropriate marital conduct." In her divorce response, Cavallari claimed Cutler "is guilty of such inappropriate marital conduct as renders further cohabitation unsafe and improper."
Cavallari and Cutler announced their split on Instagram on April 26 explaining, "We have nothing but love and respect for one another and are deeply grateful for the years shared, memories made, and the children we are so proud of. This is just the situation of two people growing apart."