"Maya is about to be 12, so she's getting pretty good with the baby," said Hawke, referring to his and wife Ryan Shawhughes's 19-month-old, Clementine.
And Hawke, like any busy parent, could use the extra hand. Besides being dad to three – his other child is son Levon Roan, 8 – Hawke, 39, plays a crooked cop in the new movie Brooklyn's Finest and has directed a new New York revival of Sam Shepard's 1985 A Lie of the Mind, which is both critically acclaimed and sold-out.
Speaking to PEOPLE at Tuesday's Manhattan premiere of Brooklyn's Finest, Hawke said that adjusting his schedule can be difficult. "Anybody who is a parent who wants to have a professional life knows that," Hawke says. "It's a struggle ... always a balance."
Calling himself "a student of acting," Hawke finds himself especially invested in the success of A Lie of the Mind. "I've worked hard on this project," he says. "It's just been just awesome. So to have it go well means a lot to me."