Actress Alma Cuervo plays an inspiring figure in young Gloria Estefan’s life in the national tour of the jukebox musical On Your Feet!, playing at Playhouse Square through Dec. 23.

She plays Gloria’s grandmother Consuelo in the musical, which tells Gloria and Emilio Estefan’s immigrant journey from anonymity in Cuba to superstardom in the United States.

“It’s really a love story, and it also deals a lot with the conflict between Gloria and her mother [Gloria Fajardo],” Cuervo said by phone from the tour in Houston.

The musical follows the love story between Gloria and Emilio Estefan, who meet in Miami when she’s a late teen and he’s in his early ’20s when she sings for his band, the Miami Latin Boys.

“They’re trying to make it as an immigrant couple who works really, really hard and there are attempts to cross over in their music, to make a hybrid of their culture in their music,’’ later becoming the Miami Sound Machine, Cuervo said.

Gloria’s mother didn’t approve of her daughter choosing a music career and wants her to instead follow a traditional career.

They become estranged but Gloria’s grandmother, with whom Gloria also grew up with in Little Havana, Miami, is steadfast in her support of Gloria.

“She’s kind of a terrific character because she was Gloria’s inspiration and her support through all this,’’ Cuervo said.

The actress, who played the role on Broadway, said she has been with the show since the beginning, since its first reading in 2014.

Cuervo, 66, who is Spanish, hails from Tampa, Fla. Her own relatives came to the United States through Cuba. She said it was particularly important for her to do the On Your Feet! tour as a part of a cast that knows Latin culture. A number of the cast members hail from Miami and Tampa, both cities heavy with Cuban influence, she said.

“It’s not just funny, it’s authentic,’’ Cuervo said of the show. “So even when we kid about it and make fun of it, we are staying within what’s real.”

Gloria Estefan’s mother fled Cuba with her when she was a toddler, forced to leave her husband, Jose Fajardo, who was imprisoned by communist dictator Fidel Castro. Jose, who had been a military policeman under Cuban dictator Fulgencio Batista in Cuba, later joined the family in Miami and fought for the United States in Vietnam.

“On Your Feet’s story of immigration is especially meaningful today,” Cuervo said.

“It also deals a lot with being from another culture and trying to assimilate in this country. It seems like every month we have reasons for it to resonate wherever we play, just with all that’s going on in the country right now,’’ she said.

The musical’s score includes smash hits such as Conga, Anything For You, Get On Your Feet, 1-2-3 and much more by the Estefans, who have won a combined 26 Grammy Awards. It also features an original song written by Gloria and her daughter, Emily Estefan.

The show features Latin dance by choreographer Serge Trujillo and an onstage band that includes members of the original Miami Sound Machine.

By the end of the first act, the whole audience is conga-ing in the aisles of this uplifting show.

“It’s authentic and it’s her arrangements,” Cuervo said of Gloria Estefan’s orchestrations.

Estefan became the first Cuban American awarded a Kennedy Center Honor on Sunday night, honored along with singer Lionel Richie, hip-hop artist LL Cool J, TV producer Norman Lear and dancer Carmen de Lavallade. Members of the On Your Feet! cast performed at the awards ceremony in Washington, D.C.

The show’s national tour had a preview week in late September in Buffalo, N.Y., and opened in the Estefans’ hometown of Miami Oct. 5.

It runs 80 weeks in 61 cities.

Arts writer Kerry Clawson may be reached at 330-996-3527 or Follow her at @KerryClawsonABJ or