When Quiara Alegría Hudes was growing up in Philadelphia, in the nineteen-eighties, her Puerto Rican mother would blast Afro-Caribbean tracks “every morning, volume eleven.” On weekends, she’d catch the bus to Manhattan to visit her aunt Linda, the composer and keyboardist for the Big Apple Circus. Linda taught her to read music, and let her turn the pages of the piano scores during rehearsal. Linda’s husband was the circus’s bandleader, and he would take the young Hudes to Tower Records to pick out tapes—blues, Bach, gospel—which she would learn to play by ear. “Around my mom, Bach was my secret,” Hudes told me recently, in a tiny room with a piano at Chelsea Studios, where she was rehearsing her new musical. Hudes has a concentrated, intellectual bearing; she speaks intently, and with considerable speed. Her parents split when she was young; on monthly visits to her dad, who was Jewish, she said, she hid her Juan Luis Guerra tapes. She studied music composition at Yale, becoming the first in her family to attend college, but she was mocked, she told me, when she wanted to practice Celina y Reutilio montunos alongside Chopin nocturnes. She had written plays as a child, so she took up theatre as an extracurricular, composing musicals based on the Yoruba pantheon that her mother had taught her. Did she feel a bifurcation in her identity? “It was at least a quatrification.”

Out of those disparate influences, Hudes has created an exceptional body of work, at once lyrical and colloquial, playful and spiritual, which often portrays wounded people on the margins (addicts, abuse survivors, disabled veterans, abandoned children) and creates spaces (a dive bar, a chat room, a road trip, a soup kitchen) where they can start to heal each other. “Elliot, a Soldier’s Fugue,” which she began writing while finishing her M.F.A. at Brown, sets monologues by three generations of veterans to the contrapuntal structure of a Bach fugue. It became the first part of a trilogy: “Water by the Spoonful,” which won the Pulitzer Prize for Drama, in 2012, uses the dissonance of late Coltrane as a kind of sonic metaphor for the painful recoveries endured by both addicts and returning soldiers, and “The Happiest Song Plays Last” celebrates community activism in the U.S. and the Middle East with the strains of Puerto Rican jíbaro music. In between the first two of those plays, Hudes wrote the book for Lin-Manuel Miranda’s musical “In the Heights”; a producer had introduced them, in 2004. Hudes, Miranda told me, turned a barrio love story into a chronicle of the Washington Heights Latinx community, resilient and ebullient under the pressure of gentrification. “She’s taking a page from August Wilson,” Paula Vogel, Hudes’s mentor at Brown and a Pulitzer winner herself, said. “She’s focussing on her ancestors and creating a canon: the American landscape with a Puerto Rican voice.”

Hudes’s new musical, “Miss You Like Hell,” is now in previews at the Public Theatre in New York; it opens April 10th. Hudes wrote the book, adapting her loosely autobiographical play “26 Miles,” about a mother-daughter road trip, and tapped the singer-songwriter Erin McKeown to compose the music, a propulsive Americana soundscape that evokes an FM dial tuning into stations across the country: folk, swing, glam rock, jazz. (They wrote the lyrics together, swapping songs for inspiration.) The story centers on Beatriz (Daphne Rubin-Vega), an undocumented Mexican immigrant who, after losing custody of her daughter, Olivia (Gizel Jiménez), to the girl’s white father, has fled to California. Four years later, when the musical begins, she has just seen a photo on her daughter’s blog—a selfie with a suicide threat scribbled on her stomach. She swoops into Philadelphia to spirit Olivia away in a Datsun pickup. On the itinerary: rescue Olivia from depression, repair their relationship, and enlist Olivia to testify at her deportation hearing (an eighteen-year-old marijuana charge has put her immigration status in jeopardy). Along the way, they encounter a Peruvian tamale seller, a Southern gay couple, an African-American park ranger—ensemble members who help them navigate the justice system. They’re a makeshift family of travellers on the margins, laying claim to the canonical territory of, as Olivia serenades it, “the mythical, the difficult, the derelict American road.”

Hudes said that the animating impulse was to “write the two thorniest, meatiest, juiciest, funniest, realest women characters” that she and McKeown could think of. Olivia wears combat boots, eschews showers, plays Chopin, hands out condoms, and totes the collected Ginsberg like a hymnal. And Beatriz is a marvel: desperate, joyous, self-dramatizing, sensual, an artist in her own right—in short, she’s Daphne Rubin-Vega, a twenty-year Broadway veteran and two-time Tony nominee who originated the role of Mimi in “Rent.” “She was the first Latina I’d ever seen onstage,” Hudes recalled, of that production. “We never heard the part in any other voice.”

All-female teams are still a rarity in musicals; Lisa Kron and Jeanine Tesori remain the only pair of women whose score, for “Fun Home,” has won a Tony. (That show also came from the Public.) With a woman also directing “Miss You Like Hell,” “there’s a lot of amazing female juju in that room,” Rubin-Vega said. She told Hudes that she was worried about giving Beatriz her all, having heard, in the past, that she was “too much” for certain roles. “You don’t have to subdue yourself,” Hudes reassured her. “You don’t have to play the model minority. The difference is, this is our space.”

Creating spaces for women to collaborate is not only an artistic goal for Hudes but also a spiritual practice. Her mother is a Lukumí priestess who told Hudes stories about her journey as a spirit medium: talking to ancestors, experiencing possession, seeing deaths before they occurred. Hudes didn’t share those experiences, but, she explained, “The listening part of me would be telling the skeptical part of me, ‘Shut up or you’re not going to learn anything.’ ” As an undergraduate, Hudes read Ntozake Shange’s choreopoem “for colored girls who have considered suicide / when the rainbow is enuf,” and was floored. “It was the first time I encountered, outside my mom’s sphere, someone else whose world vision centered around women’s healing abilities.” When she began collaborating with McKeown on “Miss You Like Hell,” she read her the end of Shange’s piece, which celebrates “a layin on of hands,” and they decided that ritual would provide the show’s climax.

The musical begins with Beatriz praying to her ancestors for the strength to reconnect with her daughter—a way to “disorient the audience from the traditional secular space that New York theatre occupies,” Hudes told me, “and say, ‘No, this woman is going to summon her spirits.’ ” Olivia is wary of the absent parent she calls “the Michelangelo of self-interest.” Beatriz tells her, “I speak Spanish, bohemian, barrio, and Caucasian. Listen and learn.” Olivia retorts, “How about ‘mother’? Are you fluent in that language?” “Which dialect?” Beatriz shoots back. “Selfless martyr or narcissistic monster?” You’ve seen mother-daughter squabbles before, but you probably haven’t seen one that hinges on interpreting Rubens’s painting of Prometheus having his liver ripped out by an eagle. (Beatriz: “Life is the eagle, not me.” Olivia: “Either way, it’s my liver.”) McKeown and Hudes brainstormed conflicting ideals of motherhood, and McKeown set their phrases to a tricky compound beat. Beatriz: “Daughters second-guess all the things that mothers do.” Olivia: “Our lady of contradictions, how shall we pray to you?”

Though their scenes are intimate, their songs have national echoes. Early in the show, a cop pulls Beatriz over, and Olivia manages her anxiety by chanting a reverse-alphabetical bibliography of her favorite literature, from Zora Neale Hurston to “The Adventures of Tom Sawyer.” Beatriz sings a ballad, “Over My Shoulder,” that traces the precariousness of undocumented motherhood in aching half-rhymes: “You don’t know if you’ll ever hold her, / The distance of love is the cruellest of borders.” Hudes witnessed such cruelties as a child. Her mother founded a women’s-health center—one night, she scooped Hudes up out of bed, drove her to North Philly, and told her to wait while she helped a woman in labor who wouldn’t go to a hospital for fear of being deported. In “Miss You Like Hell,” Olivia, through rest stops, hookups, and cagey heart-to-hearts, gradually opens up to something like grace. After her mother teaches her to drive, on the road to Yellowstone, Olivia exults in a jumble of American journeys: “Monarch butterflies take the A train / Moby-Dick swims the Great Plains / Kitty Hawk decides to bike it / The world is upside down and I like it.”

Hudes said that some of her Puerto Rican relatives told her that immigration isn’t really their fight. She doesn’t see it that way. “Choosing an immigration story is a direct response to being part of a Latino community that, by luck of the draw, happens to get citizenship rights, and wondering what to do with that privilege,” she said. “Miss You Like Hell” premièred a few days before the 2016 Presidential election, at the La Jolla Playhouse, a short drive from Friendship Park, where the Mexican-border wall divides San Diego and Tijuana. The company visited the park during workshops and saw sundered families touching fingers through the wire fence. After November 8th, the atmosphere at the theatre had palpably changed. “The feeling in the room, the first day after Trump was elected, the clenching of your heart muscles that happened—it completely rearranged the experience,” the director, Lear deBessonet, told me.

“Quiara’s in touch with spirits,” Miranda wrote to me, in an e-mail. “You have to remember, this is a woman who went into playwriting because she sensed that her family stories—those in Puerto Rico, those in Philadelphia—would fade if she did not give them language.” Hudes is now wrapping up the screenplay for a “Heights” film, and is finishing a memoir about her Philadelphia adolescence, an era when, she recalled, “I was seeing aids and drugs take down good people that I loved, and on the heels of that came mass incarceration, and it was like we were still scraping ourselves off the ground.” While she was interviewing relatives about addiction for “Water by the Spoonful,” she saw a cousin who lived next door get arrested; a few years later, she received a package from her incarcerated cousin that contained the manuscript of his first novel. Together, they started Emancipated Stories, which uses Instagram to publish pages from writers behind bars. Miranda has also dragged Hudes onto Twitter, which, she said with a grin, makes her feel like her high-school self, “because it’s a new way to play with words.” (A recent tweet: “Turn words on their head, electrify em, fire-hose em, explode em, jack open the hydrant of syntax & syllables.”) As rehearsals wrapped up for “Miss You Like Hell,” Hudes appeared to have found her space. Heading into tech week, she tweeted, “Perfect morning. Practiced Mozart on piano. Then blasted ‪@IvyQueenDiva Amame o Matame at volume 11. I am my full self now.”