The former couple announced their decision to divorce on Instagram Sunday, but a source tells PEOPLE the two had discussed whether or not to split for some time now.
"They have had divorce talks back and forth for a while," says the source. "They didn't want to get a divorce, because of the kids. Kristin has been very torn about it."
Cavallari and Cutler share three children: sons Camden, 7, and Jaxon, 5, and daughter Saylor, 4. Now that their relationship is over, the source says the reality star is focused on moving forward in the best way possible for their kids.
"When she realized that it just wasn't possible for them to stay married, her focus was on keeping things amicable," says the source.
In her divorce filing obtained by PEOPLE, Cavallari asked that the court make her "the primary residential custodian" of their kids, with "reasonable periods of parenting time" for Cutler — despite the former NFL star's request to make the two "joint custodians and joint decision-makers."
"She wants full custody of the kids, because she feels she is able to provide the most stable environment for them," says the source. "Kristin is strong and confident. She is also an amazing mom. If Jay wants to break their deal about keeping things amicable, she is not scared of fighting for what she wants for their kids."
Still, Cavallari wants Cutler in the kids' lives "as much as possible," adds the source.
"Just because she wants full custody, it doesn't mean she doesn't want Jay to spend time with the kids," says the source. "She just thinks the kids are better off living with her."
Reps for Cavallari, 33, and Cutler, 36, did not immediately respond to PEOPLE's requests for comment.
As for the grounds of separation, Cutler cited "irreconcilable differences" in his complaint, while Cavallari cited both "irreconcilable differences" and "inappropriate marital conduct." They disagree on when they formally split; she listed their date of separation as April 7, the day they returned back to the U.S. after spending several weeks in the Bahamas amid the coronavirus pandemic, and he listed April 21, the day he filed the paperwork.
In her filing, Cavallari submitted that "any misconduct alleged or implied against her" in Cutler's divorce petition "was in response to and/or as a result of misconduct on [Cutler's] behalf," though Cutler did not allege misconduct against Cavallari in his filing.
The Hills and Laguna Beach alumna and Cutler announced their split with a joint statement: "With great sadness, after 10 years together we have come to a loving conclusion to get a divorce," they said. "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. We ask everyone to respect our privacy as we navigate this difficult time within our family."