Diablo Cody is writing her way through life’s transitions, from a girl evolving into a grown-up in “Juno” to a woman refusing to let go of her teenage years in “Young Adult” to a mother watching parenthood close the door on her youth in her new movie, “Tully.”

The screenwriter’s latest film, opening Friday, stars Charlize Theron as Marlo, a sleep-deprived mother of three who hires a nurse to handle the night shift with her new baby. Marlo is at risk of getting swallowed up whole by motherhood. Enter Tully, the nanny played...