November 11, 2014 06:00 PM

Gregg DeGuire/WireImage

Saturday’s Governors Awards made for an unusual date night for Mark Wahlberg and his wife Rhea Durham: joining the couple was their eldest daughter Ella.

But attending parties with their parents is a rarity for the 11-year-old and her siblings, Michael, 8, Brendan, 6, and Grace, 4.

“I don’t try to bring them to too many events,” Wahlberg told PEOPLE Monday at the world premiere of The Gambler at AFI Fest 2014 presented by Audi in Los Angeles.

Although parties aren’t usually on the agenda, the children can’t pass up a visit to see Wahlberg on set.

“They like to raid the craft service and play in the trailers,” he explains. “They had a lot of fun on Ted 2 because we had this great big set built at the Fox lot and they literally had the run of the place.”

However, going behind the scenes is typically the only chance Wahlberg’s kids get to see their famous father at work.

“They don’t understand why they can’t see Ted because they think, ‘Oh, it’s just you and a teddy bear, Dad.’ They want to see everything that I do, but obviously it’s not appropriate,” Wahlberg, 43, shares.

But the foursome have carved out a special hour to soak up time with the actor — one that’s landing Wahlberg in some hot water.

“My wife is getting upset because my kids are waking up at 4:30 in the morning on school days to come and hang out with me in the gym,” he explains. “The teacher’s writing notes saying, ‘[At] 1 o’clock they’re falling asleep in the classroom. What’s going on?’ So I’m in big trouble for that.”

— Abby Stern

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