Preston Max Allen’s perceptive, keenly observant, and ultimately moving play Caroline begins ordinarily enough. A mother and daughter are ordering mac and cheese and French toast at a diner. The daughter, aged about 10, has a cast on her arm. The mother explains they have a long car trip ahead of them. The daughter attempts to manipulate her mom into buying her a Switch video game console, using her injury as leverage. The mother puts off the decision. Allen slowly, skillfully reveals the deeper story during this seemingly mundane scene and the one that follows in a motel room. The child, Caroline, is trans, and the two are leaving West Virginia, partially because of its harsh laws against gender-affirmative care for minors, and partly because of the mother’s abusive boyfriend. The mother, Maddie, a recovering alcoholic and drug addict, plans to visit her long-estranged parents in Evanston, Illinois, to ask for help.

Over the course of 90 minutes, Allen and his dedicated cast unpack the complex relations between three generations of a dysfunctional family, ravaged by addiction and coping with the thorny issue of gender fluidity. David Cromer’s simple direct staging allows the three performers to deliver credible, unstagey performances, free of melodramatic excess.

Chloë Grace Moretz endows Maddie with an intense desperation to do the right thing for Caroline while also expressing the character’s frustration over her impossible situation and her regret for making so many bad choices. Amy Landecker as Maddie’s elegant mother Rhea is all frosty reserve and barely contained rage at Maddie for her crime-and drug-saturated past which made her parents’ life hell. Allen makes it clear no one is a villain here, he presents each character as complex and their motivations are understandable if not entirely justifiable. (Maddie’s father is conveniently out of town on a business trip, so the play remains a three-hander. Landecker also plays a waitress in the first scene.) Interestingly, Landecker played the daughter of a transgender father in the groundbreaking Amazon Prime series Transparent. River Lipe-Smith gives an assured and mature performance as the title character, perhaps one of the best I’ve seen given by a child actor, convincingly conveying Caroline’s intelligence, vulnerability and confidence in their identity.

The challenges of raising a transgender minor child are compassionately explored. In a bold move, Allen does not make Caroline’s gender issues a source of conflict between Maddie and Rhea. (Their conflict lies in strongly disagreeing over who knows best what’s for the child.) Rhea is surprisingly nonplussed when Maddie informs her of the news (Maddie left her parents’ lives well before Caroline was born). “We’re not Republicans,” Rhea almost off-handedly remarks in defense of her total acceptance of her grandchild identifying as trans. At the performance attended, the audience responded with laughter and applause. I didn’t quite buy that Rhea would be so open so quickly to such a difficult adjustment, but this is the play’s only flaw.

Lee Jellinek designed the suggestive, flowing sets which transform from the diner and motel into Rhea’s comfortable suburban home with the aide of Tyler Micoleau’s mood-changing lighting and Cromer’s sensitive, flowing direction. Caroline is an understated, seemingly small play about big emotions, delicately and sensitively handled.

Sept. 30—Nov. 16. MCC Theater at the Robert W. Wilson MCC Theater Space, 511 W. 52nd St., NYC. Running time: 90 mins. with no intermission. mcctheater.org.