By Mary Margaret

04/25/2013 at 10:35 PM EDT

Jessica Ussery and Jason Aldean

Bauer-Griffin

Are Jason Aldean and Jessica Ussery heading for a split?

“I can confirm that Jason and his wife are having problems, but there is nothing more to share with the press at this time,” his rep tells PEOPLE when asked if the couple have called it quits. “It’s a private family matter, and we hope everyone will respect that he would like to keep it that way.”

Last fall, Aldean issued a public apology after he was photographed being affectionate with season 11 American Idol contestant Brittany Kerr.

Despite the setback, the singer was confident that the future with his wife was a bright one.

“This year … the good stuff has definitely outweighed the bad,” he told PEOPLE in December. “All that other stuff is kind of in the past and we’re just looking to have a great year in 2013.”

Ussery and Aldean, whose romance began in high school, have been married since 2001. They have two daughters together – Keeley, 10, and Kendyl, 5 – and had been working through their issues.

“The main thing is that me and my family are okay, and everything’s good there,” he insisted shortly after photos of his inappropriate behavior were published.

In March, Ussery was at Aldean’s concert at New York City’s Madison Square Garden – and spotted sitting on her husband’s lap at the after party.

But at the Academy of Country Music Awards earlier this month, Aldean walked the red carpet solo.