"For me, it was equal to doing family therapy in a room full of strangers," says Dylan of filming the emotional, and sometimes volatile, scenes in the movie.
She adds, "I've done family therapy, but I've never done it with a crew that I didn't know."
For Sean, 60, "there were times that I had to not only avoid going in to hug her but, in fact, push for more," he says. "I felt like somebody ought to call Child Protective Services at that point."
Simone Comi/IPA/Shutterstock Dylan and Sean Penn
metro Goldwyn-Mayer Pictures Inc. Dylan and Sean Penn in Flag Day
Dylan's other famous parent, actress Robin Wright, was a big factor in Dylan's decision to work with her father.
"She very simply said, 'I've never worked with a better director than your dad. It was the most amazing experience I've ever had as an actor,'" Dylan recalls. "So I trusted that."
Dylan also reveals the best advice she's received from Sean: "Don't do anything that feels false, because if it feels unnatural, it's going to read onscreen."
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Flag Day, based on Jennifer Vogle's 2004 memoir, follows a young journalist's conflicted relationship with her con artist father. Sean plays the dad, while Dylan and his son Hopper, 27, play his children.
"We've always been close, but working together only enhanced my belief that I can always fall back on him," says Dylan.
For more about Sean and Dylan Penn, pick up the latest issue of PEOPLE, on newsstands Friday.