Kristin Cavallari and Jay Cutler have filed divorce papers.

In the documents obtained by PEOPLE one day after the couple announced their split, Cavallari, 33, cites both "irreconcilable differences" and "inappropriate marital conduct" as grounds for the breakup. The reality star lists 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. Cutler, 36, simply lists "irreconcilable differences" as grounds for the divorce and lists their date of separation as April 21.

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In her filing, Cavallari claims Cutler "is guilty of such inappropriate marital conduct as renders further cohabitation unsafe and improper."

She also submits 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 does not allege misconduct against Cavallari in his filing.

Cavallari is seeking primary physical custody of their sons Camden, 7, Jaxon, 5, and daughter Saylor, 4, with "reasonable periods of parenting time" for Cutler. Cutler is seeking joint custody of the kids.

In his petition, which was filed first, Cutler states that he "has always been the available at home parent and primary caretaker" of their children, which Cavallari denies in her response, saying that she "has been the primary residential parent."

Cavallari is asking for child support and that Cutler pay for their kids' health insurance. TMZ first reported the news of the filings.

Image zoom Jason LaVeris/Getty

The Hills and Laguna Beach alumna and former Chicago Bears quarterback started dating in 2010 and wed in 2013. They currently reside outside Nashville, Tennessee, and have documented their relationship on Cavallari's E! reality show, Very Cavallari.

On Sunday, the stars released a joint statement on Instagram: "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."

A source told PEOPLE that the timing of the split — as people around the world shelter at home to stop the spread of the coronavirus — was purposeful.

"The reason they announced it now is because it's a quiet time for them to work through all of this and try to move forward," the source said, adding that they were already planning to part ways before flying to the Bahamas.

"On their recent trip, they already knew they were splitting up," the source said. "Kristin and Jay had been having problems for a long time. They hadn't spent much time together in recent months."

The source also said the breakup had "absolutely nothing to do" with the rumor that Cutler had an affair with Cavallari's ex-BFF, Kelly Henderson. According to the source, Cavallari and Cutler are simply very "different" and grew apart.