updated 03/27/2014 AT 7:00 AM ET
•originally published 03/26/2014 AT 4:45 PM ET
The country singer’s wife of 16 years, Rhonda, filed papers in Tennessee on Tuesday, citing “irreconcilable differences,” WSMV reports.
“Trace and Rhonda are united in ensuring that their children’s interests come first. They thank everyone for respecting their privacy as they work through this personal matter together,” the singer’s rep tells PEOPLE in a statement.
Rhonda is asking for primary custody of the couple’s three daughters – MacKenzie, Brianna and Trinity – and for Adkins, 52, to pay child support, alimony and all her legal fees.
Adkins, who has battled alcohol addiction in the past, spent time in rehab in January after getting into an argument with a Trace Adkins impersonator on a cruise ship.
He left treatment in February to fly to Louisiana when his father, Aaron, 71, became ill, but his dad died a few days later. After his father’s passing, Adkins returned to complete his treatment program.
Adkins’s rep did not return calls for comment.