As a young girl growing up in LA, sunny as her surroundings, Viveca takes on two things in particular: the shooting of four black children in an Alabama church, splashed over the front pages, and the whiteness of her favourite doll, Chitty Chatty. Bad things, she assumes, come with blackness. "I've decided I'm going to be white."

First seen off-Broadway way back in 2000, Kirsten Childs' semi-autobiographical musical tumbles through the second half of the 20th century, but it only skims the surface of history. Most of us do. History rubs off on us. We're shaped in cultural currents.

Viveca more than most. She's an impressionable soul who dreams of being a dancer, and Childs details a lifelong struggle with herself: how black to be and how to be black. All her life, she bumps into white cultural norms, standards of beauty and social etiquette. At high school she's dismissed as an ‘oreo' - white on the inside - but when she tries to take ownership of her race and roots, it feels all the more artificial. Karis Jack, a fine physical comedian, squirms though a party as she plays it cool. Her politics and her tastes, she picks up from others, protesting with hippies, then diving headfirst into the disco scene. If the times are a-changing, so's Viveca - and so's what it is to be black. Her hair straightens and curls through the years.

One moment cuts to the quick. Walking home, her date's stopped by police and held, on his knees, at gunpoint. "Wrong one," says the cop and, in that moment, there's no ignoring how much appearances matter when you're judged by your skin tone.

The dilemma is that of assimilation: how to succeed as a black woman when success is defined by white standards. It's not just that her light-skinned dance classmate gets cast in the lead, it's that ballet wasn't built for black bodies. "Tuck that butt in," her childhood teacher tuts. The same problems recur later in life and Viveca, now played by Sophia Mackay, finds herself sidelined to ‘sassy sidekick' roles. At auditions in New York, she performs her blackness, conforming to cliché. Overdoing it somewhat, Mackay drops into a knock-kneed, lickspittin' cartoon – an adopted minstrelsy, really. She gets the job.

Childs makes her point formally. Her musical is so relentlessly bubbly it very nearly bursts. She keeps it light at all costs, pushing history to one side, as if trying to wrestle romance into focus, not race relations. It's just as restless as she is, churning through song styles as she tries on new looks; most of them peppy, poppy and white. Only at the end do both find their voice. Viveca stops smiling and speaks out. Mackay plays it beautifully: her shoulders drop, her face relaxes and she seems to breathe properly for the first time.

Josette Bushell-Mingo's production never really delivers through. It's intent on easy laughs, stuffed with cheap gags and gurns, but she never sours that laughter. Instead, everything's so eager to please – both strange and a shame, given that that's precisely what Childs critiques. Rosa Maggiora's plasticky design is pure Nickelodeon, and many of the supporting performances go out of their way for laughs. Only Trevor A Toussaint and Sharon Wattis hold back as Viveca's parents, but Childs encourages comic exaggerations and one leaves with the sense that, at the time of writing, she still wasn't being true to herself.

Click here to watch our video with the cast

The Bubbly Black Girl Sheds Her Chameleon Skin runs at the Theatre Royal Stratford East until 11 March, and at the Belgrade Theatre, Coventry from 5 to 15 April.