Boil down the message of Christopher Shinn’s Lincoln Center two-hander “Dying City” and you wind up with a familiar theme. Bad parents warp their kids. Let the psychoanalytic camps slap each other with the nature versus nurture paddles if they must, but a quarter-century of doggedly insistent “Oprah Winfrey” specials can’t be wrong. Look behind the man mistreating you today, you’ll find a bad dad throwing punches in the past. At its heart, therefore, the psychology of “Dying City” is hugely reductive.

But Mr. Shinn wants to demonstrate that crappy parenting also happens on a national scale. Despite scarcely a word uttered directly about Iraq, Mr. Shinn’s domestic drama insists that any endeavor twisted at the root is doomed to be twisted in the branch.

A year previous to the play’s start, therapist Kelly (Rebecca Brooksher) lost her army reservist husband Craig (Pablo Schreiber) in the Gulf. Now his identical twin Peter (Mr. Schreiber, again) has shown up unexpectedly at her apartment door, insisting that she share a grief she would clearly rather forget. Peter hasn’t processed his bereavement well — that very evening he has walked off stage, ditching his fellow actors in the middle of a Broadway show, and once in Kelly’s living room, he refuses to obey her many efforts to oust him. When he does wander offstage (usually to check his voicemail), Kelly relives Craig’s last, chaotic night at home, when the threesome’s dysfunctional fraternal and conjugal bonds started to show serious strain.

On his final evening in New York, the sullen Craig slams around the apartment, clearly preoccupied with his coming deployment. But he spares time to viciously undercut his wife’s professional abilities, insult his brother, and pick a number of escalating, pointless fights. As scenes with Peter alternate with Kelly’s flashbacks, resemblances emerge between the brothers. Both demand that Kelly face ugly truths about Craig, both play manipulative games with her that she, the expert, can’t seem to penetrate. And despite a couple of narrative feints, the three of them drive inexorably toward a recognition of how awful childhoods have shaped Craig’s ugly character, Peter’s slyness, and Kelly’s seemingly bottomless victimhood.

Mr. Shinn operates as a latter-day Mendel — by showing us twin strains of the same plant, he investigates the effects of their mutations. On the surface, Peter is the gay actor, who is dominated by his brother and desperate for affection. Craig is straight and married, and swaggers about, apparently confident in both his strength and his brains. Ms. Brooksher has to deliver the clunky explanation (“ROTC got him through Harvard!”), but it is only Mr. Schreiber’s brutal performance that makes us believe both are possible. Even as the puppyish, indirect Peter, his presence feels like a home invasion. That his weapons are a sheaf of email printouts makes him no less a thug.

As he did in “Where Do We Live,” Mr. Shinn continues to use the events of September 11, 2001, as a touchstone for his characters — for Craig and Kelly, the falling towers are the last symbol of their togetherness. The milquetoast Kelly, drawn so thin she must be a symbol, is the New Yorker nostalgic for 2001, when tragedy at least made things clear. Since then she has been lied to, cheated on, and left behind by a suicidal military mission.

She should sound familiar. If Ms. Brooksher’s performance sometimes seems glassy, it’s only because Mr. Shinn uses her just as ruthlessly as the twins do. She must simultaneously reflect each man’s misdeeds and her playwright’s contemporary pathos — it would be too much to expect a glorified mirror to become three-dimensional.

The ambitions Mr. Shinn has for his piece, its allegorical efforts, and his evident technical grace should make “Dying City” something more than it is. Director James MacDonald keeps the twin trickery moving swiftly and seamlessly, and he drags the maximum menace out of Mr. Schreiber. Setting it on Anthony Ward’s gently rotating stage, he subtly adds to Mr. Shinn’s already respectable pace. But nothing can substitute for poetry. Just as with Mr. Ward’s roundtable, it may escape us for a while, but eventually we notice the machinery moving.

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