Jon has shared physical custody of the kids, while Kate maintains full legal custody.
"The call came in at 1:10 this afternoon for a verbal domestic argument ... over the custody of one of their 13-year-old daughters," the rep said.
"No one was arrested and the daughter did go home with the father after she expressed that was her desire to do so."
Kate and Jon share 16-year-old twins Cara and Mady, and 13-year-old sextuplets Aaden, Alexis, Collin, Hannah, Joel and Leah.
The pair divorced in 2009, and have battled for custody of their children since.
"I haven't seen all my kids together in about three years," Jon said in an interview with "The Steve Harvey Show" in January 2016. "I only get what I get ... whoever comes down the driveway, that's who I get."
"I'm not privy to any information," he claimed. "There's no co-parenting. She parents, I parent. I would love to co-parent, but at this point in time, I don't see it happening."
Kate and Jon came to fame on the TLC series "Jon & Kate Plus 8," which was renamed "Kate Plus 8" after the pair's divorce.
Kate and the kids continue to star on the show, while Jon has worked as a DJ and a stripper.
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