While I’m not sure I can point to a precise moment when Qui Nguyen’s “Poor Yella Rednecks” won me over, it may have been near the end of Act One, when a puppet launches into an acrobatic martial arts routine set to “Eye of the Tiger,” the theme song from “Rocky III.”

Until that point, “Rednecks” — Mr. Nguyen’s follow-up to “Vietgone,” which recounted how his Vietnamese-born parents met at a resettlement camp in Arkansas after fleeing their war-torn homeland in the 1970s — struck me as a little goofy, and not in the positive, deliberate sense. Picking up when his mother, Tong, and father, Quang, decide to get married, the new play — like “Vietgone,” a comedy — traces their trials and foibles as they adapt to life in the predominantly white town of El Dorado. 

The couple is joined by Tong’s mother, Huong, an aggressively feisty woman whom her son-in-law describes at one point as “like Charles Manson, but meaner.” As Tong and Quang confront challenges stemming from racial bigotry and their limited English — not to mention a first wife Quang left behind — we meet a succession of mostly minor American characters, whose language and culture are represented with references to Batman, Burger King, and notorious political and media figures. (The last, which include Mitch McConnell and Tucker Carlson, tend to be anachronistic.)

More prominently, there’s Tong and Quang’s son, 5-year-old Little Man, embodied by that cute puppet — designed by David Valentine and maneuvered by Jon Norman Schneider, who also appears as the grown playwright. In that “Rocky”-inspired scene, Huong teaches Little Man to defend himself against school bullies, as William Carlos Angulo’s choreography and Shane Rettig’s sound design wink and nod to the bionic hero of the ’70s TV series “The Six Million Dollar Man.”

Mr. Rettig also provides music for a string of sporadically charming, if not especially clever, rap numbers, one of which borrows a line from “Hamilton.” Mr. Nguyen, whose credits also include work for Disney and Marvel Studios, and director May Adrales enhance the action visually with cartoon projections (designed by Jared Mezzocchi) and playful animated effects.

Yet it’s the heart underlying these shenanigans that ultimately propels “Rednecks” beyond its initial silliness. As Tong and Quang, Maureen Sebastian and Ben Levin not only make a very attractive couple but, as Mr. Nguyen’s dialogue offers them a little more meat in Act Two, they capture the difficulty of sustaining patience and trust under pressing circumstances.

Samantha Quan’s portrayal of Huong, likewise, grows richer as the role evolves into less of a caricature. When Little Man, toward the end of the play, questions whether one of her accounts of Vietnam’s grandeur is true, Huong relies, “Well, it’s a story. And stories are all that matter in this world because it’s the only things we get to keep in our hearts.”   

Plainly, this power was not just on Mr. Nguyen, and “Poor Yella Rednecks,” for all of its corniness and other imperfections, proves a touching testament to an artist’s love for his family and heritage.