The air hangs heavy in Alma, a drinking club in 1950s Port of Spain, Trinidad. Heat and rum bring their own kind of languor – but in Martina Laird’s play, change is coming, both within a fractured family and in the wider world.

Alma is managed by a mother and daughter. Ellen Thomas gives the indomitable Pearl a basilisk glare but not maternal instincts (“the only thing I done wrong is to make children dat not worth nothing”). Ruby (an exuberant, citrussy Cat White) runs a honeypot scam on tourists, but doesn’t intend to “stay here in downtown hell”.

When Pearl’s long-abandoned son Diamond arrives, tensions seethe. The RSC’s content warnings flag up incest – so it’s no surprise when Ruby and Diamond catch each other’s glance. She stands in golden lamplight, and he draws close, moth to flame. Martins Imhangbe’s towering Diamond moves in an unhurried, proprietary roll, teetering and then rising on his toes.

Laird captures a country on the febrile brink of change. Nationalist Eric Williams (later the independent island’s first prime minister) is standing for election, urging voters to reject the claims of British rule and American economic encroachment. Calypsos with a satirical snap play between scene changes.

Alma stands for the country itself: worked by Trinidadians, but British-owned and exploited by Yankee might. The elderly English owner is an orotund bore, patronising Pearl (“my tropical nightingale”) and Ruby (“you are a beautiful bauble”). But Pearl is ready for independence: “That wind is blowing like it’s kite season!”

Laird’s first staged play, runner-up for the Verity Bargate award, still feels in need of another draft. Plot and emotion are dialled up to 11 but don’t shake you as they might. A different production might ignite the dialogue’s crackle; Justin Audibert’s heavy-handed direction sloshes in music to underscore emotive speeches and ambles towards the flickering redemption that might break the cycle of personal and political history.

Driftwood is steeped in atmosphere, enhanced by Simon Spencer’s lighting: amber gliding over ink-blue walls, or dunking late night confessions in an eerie moss green. The best of Laird’s writing is equally vivid: the tang of sour memory, the detail of dreams betrayed.

• At the Other Place, Stratford-upon-Avon, until 30 May. Then at Kiln theatre, London, 3 June-4 July