As audience members took their seats at the Tisbury Amphitheatre on Saturday morning, Fabulists’ cast member Paul Padua informed the crowd that they would be traveling together many miles from the canopy of the Tisbury trees.

“We’re now in the hottest place in the United States,” Mr. Padua announced, gazing up at the audience from his spot onstage. “The Mojave Desert.”

The desert set the scene for The Fabulists’ hour-long show­—a production filled with improv, one-liners and lots of help from the audience. The children’s theatre troupe was co-founded over 25 years ago by MJ Bruder Munafo, artistic and executive director of the Martha’s Vineyard Playhouse.

Paul Padua has been performing with the Fabulists for 26 years. — Maria Thibodeau

“We have fun. We try to be as silly as we can be,” Ms. Munafo said. “Children start coming to see the shows when they’re really little, and then we see them again when they’re grown up with children of their own.”

This journey includes cast members too, in particular the Padua family. On nearly every Saturday Paul Padua is joined onstage by his wife Magi and their two sons, 15-year-old Theo and 18-year-old Augie.

Mr. Padua began performing with the troupe in 1992. During his 26-year tenure he has played at least 50 different characters, and that’s a conservative estimate.

“Because in some shows I do more than one character,” Mr. Padua said.

Combat comedy. — Maria Thibodeau

Often he is the first to appear onstage, fulfilling the role of the narrator. He said he and his wife have always encouraged their sons’ musical and theatrical interests, and that they worked to involve them with the troupe from a young age.

“Augie was born in 2000, Theo in 2003. I don’t think there were any Saturdays in July or August where they didn’t attend the show,” Mr. Padua said. “They are both musicians, so I incorporated them as the house band before they were ever on stage.”

The brothers traded in their instruments on Saturday for a set of costumes. Theo wore a feathery headpiece as roadrunner, while Augie wore a pair of large coyote ears. He slunk through the audience, attempting to hoodwink the youngsters in his path.

“I’m a man of mystery, no one knows how I do it,” Augie exclaimed as he showcased a magic trick, detaching and reattaching his thumb to his hand.

Each performance centers around a unique theme. — Maria Thibodeau

Each Fabulists’ performance centers around a unique theme, with scripts often written beforehand by a collection of cast members. Saturday’s performance was called Desert Tails, written by Ms. Munafo. The story followed the friendships of five lively Mojave Desert animals and one elderly Joshua tree.

Toby Esposito played the tree, his hair and wrists wrapped with green pipe cleaners. He told wise tales and cracked jokes with Mr. Padua, who narrated the show as an eight-legged tarantula.

“Why I remember the day you were born,” Mr. Esposito said in a drawl to Mr. Padua, pausing dramatically after each word. “That makes me feel very old.”

Also onstage were Hallie Brevetti and Ali Saiff, who played a jackrabbit and rattlesnake respectively.

Ms. Saiff, who teaches music at the West Tisbury school, carried two egg-shaped maracas, one in each hand. She shook them vigorously with every step across the stage, hissing at her castmates and the audience.

The children's theatre troupe was founded over 25 years ago. — Maria Thibodeau

“I’m looking for 10 ssssnakelets,” Ms. Saiff hissed, delighting the audience’s youngest members, who jumped out of their seats to join in on the fun. In a line, the snakelets shimmed and slithered to the beat of a song, sung by Ms. Saiff and eventually the rest of the audience.

“Slither to the left! Slither to the right! Slither, slither, slither, out of sight!” Ms. Saiff sang, hissing intermittently with every line.

Between scenes, each castmember encouraged the audience to participate in games like red light, green light, follow the leader, and a slow-motion road race.

The Fabulists’ run at Tisbury Amphitheatre continues on consecutive Saturdays through August 25. Then it’s back to school for audiences and the Padua family. Augie begins college this September, while Paul and Theo head back to high school in New York — Theo is a student and Mr. Padua is a math teacher in the New York city public school system.

Some years the Padua family brings their summer vacation home with them to share with friends. In a 2014 Fabulists’ production of A Midsummer Night’s Dream, Mr. Padua played Puck, Mrs. Padua starred as Queen Oberina, and the boys claimed the roles of Demetrius and Lysander. Following the performance, the family posed for a picture.

“That photo became our Christmas card,” Mr. Padua said. “It said, Happy Holidays, In dramatic fashion, the Paduas.”

The Fabulists perform on Saturdays in August at 10 a.m. at the Tisbury Amphitheatre. Next week’s show is The Girl Who Would Be Princess. For more information visit