Brinkley tells PEOPLE: "You can be in absolute agony, but when you see your kids, you have to be like, 'Hey, guys!' "
Credit: Ari Michelson

These days, Christie Brinkley seems to have it all.

At 62, she’s got a hot man (singer John Mellencamp), she’s still modeling and has parlayed her all-American sex appeal into a lifestyle empire worth an estimated $80 million. (Her newest venture is a new line of organic prosecco, Bellissima, hitting stores this summer.)

But the supermodel has also overcome her share of heartache. In 2006, she faced a tabloid frenzy when it was discovered that her fourth husband, Peter Cook, was cheating with his teenage assistant. The pair fought over custody of children Jack, now 21 (Brinkley’s son with ex Ricky Taubman, whom Cook adopted at age 4), and Sailor, now 18. But Brinkley (who is also mom to Alexa Ray Joel, 30, with ex-husband Billy Joel) prefers not to dwell on dark times.

“I went through a lot,” she says. “But you have to stay strong for your kids. You can be in absolute agony, but when you see your kids, you have to be like, ‘Hey, guys!’ ”

Brinkley says she found strength from the website One Mom’s Battle, which she calls “a support group for women dealing with a narcissist” – and in performing live on Broadway during a stint in Chicago.

“For the three hours that the show was on, nothing else existed,” she says. “It was a complete escape.”

For more from Christie Brinkley, pick up this week’s issue of PEOPLE, on newsstands Friday

Overcoming the drama of her divorce may have also made Brinkley appreciate her other ex, Billy Joel, who married for the fourth time last year.

“He just sent me a video of him with his new baby, and she’s so adorable,” Brinkley says, breaking into a warm smile.

“It’s really nice that we get along so well. That’s what you want in a relationship. It’s somebody that’s been a big part of your life. That’s the way it should be.”