Viewing extreme disability produces in most people an intense discomfort. Juvenile joking about “retards” is a symptom of a deep anxiety about those who seem different. Maturity does not usually cure the underlying sense of repulsion and shame — when we see a deformed, crippled or mentally handicapped individual on the street, we tend to avert our eyes.

“Lydia” (written by Octavio Solis, directed by Juliette Carrillo) is not an easy play, mostly because neither the audience nor the characters can avert their eyes from the grotesque tragedy taking place for almost the entire three hours downstage center on a cot in the Flores family’s living room. The emotional melodrama of the rest of the show — immigrant acclimation troubles, an alcoholic and emotionally distant father, a surprise gay love affair — is fairly interesting, but it’s all pretty standard. The plot twists pale in comparison to the contorted body of the household’s youngest child, the once-beautiful Ceci (Onahoua Rodriguez), who on the eve of her Quinceañera split her head open in a horrible accident and has been reduced to a moaning, flailing vegetable. She is hard to watch, not only for her onstage family, who remember her as she was, but for the audience, who struggles with alternating sympathy and revulsion.

The play, in production now at the Yale Repertory Theatre, follows Ceci and her family two years after the accident, when they hire the beautiful Lydia (Stephanie Beatriz), an illegal immigrant from Mexico, to serve as their maid. The Flores home is in El Paso, Texas, a border town where mojados and “quasi-middle-class” immigrant families like the Flores’ inhabit a world of struggle and Spanglish. The drama takes place during the Vietnam War, foregrounding the questions of what America stands for and what makes an American.

Despite the attention paid to the family’s immigrant status, by far the more compelling stories are the relationships between the characters, which are troubled, complex and constantly evolving. Rosa (Catalina Maynard), the overworked mother, struggles to hold the family together despite the fact that her husband Claudio (Armando Duran) only seems to leave his alcohol coma to abuse her and their youngest son Misha (Carlo Alban). Rene (Tony Sancho), the older son, gets into too many fights and seems destined to die before he hits 20, in stark contrast to his cousin Alvaro (Christian Barillas), recently returned from Vietnam. Into this mix comes Lydia, who has enough love and patience to immediately connect with Ceci and eventually bring down the defenses of the entire family, often with unintended and disastrous consequences.

Like most Latin-American literature and all college students, the show is obsessed with sex. Sex — not the commercialized imitation but the complex, violent, incestuous reality shown here — rivals physical and mental deformity in its ability to make viewers intensely uncomfortable, and it is almost equally challenging to watch. Ceci describes her own sexual frustration and observations of the family in dramatic, metaphoric, passionate and sometimes baffling monologues that interrupt the main action. Actress Onahoua Rodriguez tackles the complex role with admirable energy. Still, at times it is hard to say which is more unpleasant: the flowery monologues or the contorted moans.

Parts of the show do elicit uncomplicated joy from the audience — Lydia’s sassy, broken back-talk and the exquisite, simple set are both lovely to watch. And there are plenty of moments of genuine feeling. One of the best is when Claudio, who has been trying to learn English, arrives home from work and breaks his silent anger to get belly-down on the floor next to his daughter. As she moans he says, “The only English I want to learn is yours.” This struggle to communicate the unspeakable and uncomfortable is central to “Lydia,” and the show certainly succeeds in reminding us how hard, and how important, that task is.