"One day all of it yours," says the matriarch in broken English to her grandson in Ryan Craig's new play. It sounds like a grand promise, but Yetta Solomon's rubber shop looms threateningly over her family, and in fact the stage in Edward Hall's production. It is a dark, dirty, dominating presence and in Ashley Martin-Davis's huge, oppressive designs there are layers, upon layers of rubber stuffed into shelves and dumped in corners. The shop she is so keen to keep in the family is excruciatingly overbearing, it forces the direction of this family's lives and crushes the characters' hopes.

This is the legacy of a woman who came to London on a boat with nothing; an immigrant who worked and worked on the markets with her husband before managing to buy her own place. Craig's play charts 20 years in Yetta Solomon's family – her husband dead, her sons running the business with eventual help from their own sons – from the early '60s to the early '80s. It is an epic narrative, echoing big classic American fighting family dramas.

Yetta is very much at the centre of Filthy Business. She is formidable, fazed by nothing, and has the right answer to everything. Manipulative and cunning, while being loving to those dearest to her, her raison d'etre is to ensure the shop and their livelihood will succeed at all costs. Even the cost of happiness.

Over the course of the play, pretty much everyone tries to escape Yetta's web but no-one manages to. Her son Leo, the brains behind the business, wants to set up on his own, but his plans are stamped on by his mother; Leo's son Mickey has revolutionary ideas for a business – he wants to tap into the soft furnishings markets – but she curtails that dream too. At the end of all their hopes is Yetta, both lifeline and grim reaper, because as she repeatedly stops the family from separating, the business, and their lives, slowly unravel.

Sara Kestelman, who almost stole the show on this same stage in IHo last year, plays Yetta and she is brilliant. Small in stature, but big in everything else, she is a ferocious force as she calls bullshit on everyone and everything. Kestelman brings heart and hate to the role, reflecting Yetta's simple essences: this woman sees the world through the prisms of loyalty and skill only. Even in her moments of great kindness, of which there are several, Kestelman makes sure Yetta is still seen as a pragmatist. The rest of the cast hold their own, but it's only really the enjoyable-to-watch Callum Woodhouse as grandson Mickey who manages to stand out alongside Kestelman. His journey is believable and well balanced.

Craig's narrative is very juicy, featuring twists, turns and shocks from beginning to end. But this is a big play, with a lot of characters, and where Yetta is fully fleshed, the rest are not as three dimensional. Though this doesn't spoil proceedings – there's a lot to hang on in this piece – it does mean that occasionally the focus becomes a little vague and a little crowded: the myriad themes of family, immigrant, motherhood, sacrifice, letting go of your kids and happiness are slightly too thinly drawn.

But it is Craig's evocation of an overbearing family figure, and the impact she has on the people around her, which rings most true. Yetta is so blinkered by her need to keep the family together and keep the shop open – "this is my country" - that she cannot see what and who she is destroying. It is riling, heartbreaking and often excruciating to watch.

Filthy Business runs at Hampstead Theatre until 22 April.