Burnt by the Sun, NT Lyttelton, London<br>Dancing at Lughnasa, Old Vic, London<br>As You Like It, Curve, Leicester

1936: The Great Terror looms over a Russian family gathering, while in Ireland, old certainties are crumbling

Everyone is dancing on the verandah of the Kotovs' dacha, to the strains of a passing military band. It's a national holiday and the morning light slants softly through Act One of Burnt by the Sun. This portrait of Russia in 1936, in a new adaptation by Peter Flannery, is staged by Howard Davies with an exquisite and enthralling blend of Indian-summer serenity and intensifying menace.

You might think this was a forgotten masterpiece by Chekhov. The willowy lady of the house, Michelle Dockery's Maroussia, grew up here among the pre-revolutionary intelligentsia, and her relations are still in situ. Idling at breakfast in their silk dressing gowns, they reminisce about nights at the opera, read out snippets from the newspaper, and tease their spinster-housekeeper. They themselves allude to The Cherry Orchard, yet times have moved on, dangerously.

For this is Stalin's USSR, with the Great Terror only just over the horizon, and Maroussia has married a peasant-born Red Army general. Ciaran Hinds' grizzled Sergei – with bristly Stalinesque moustache – sits in a corner like a hulking bear and listens to his in-laws' bourgeois nostalgia, giving it short shrift.

We gather, from Pravda, that trials have begun in Moscow to purge the so-called enemies of communism, and then suddenly Rory Kinnear's Mitia – the great love of Maroussia's youth –reappears after 12 mysterious years away. He acts the joker, saying he has merely been working as a cabaret pianist in Europe, but he is fraught and seems hell-bent on winning back his beloved.

I won't reveal the play's searing plot twists, as many theatre-goers won't have seen Nikita Mikhalkov's original 1990s film (co-scripted with Rustam Ibragimbekov). Suffice to say, the love triangle is enmeshed in political manoeuvres, and this piece disturbingly exposes how people, faced with social upheavals, can become treacherous lost souls, shockingly changed by regimes that obliterate their old certainties and hopes.

Davies's production is beautifully fluid, the dacha revolving slowly so you follow the characters from room to room. A few glitches arise, both in play and performance. Mitia tells an overlong allegorical fairy tale; Dockery excessively foregrounds her shock at his homecoming, jittering a vodka bottle against a glass. Overall, though, the ensemble acting is splendid, including Duncan Bell as a decadent, buttock-eyeing lawyer and Tim McMullan as a chirpy fool. There is also wonderful naturalistic detailing, and humour woven into the encroaching tragedy. See this.

Maybe Dancing at Lughnasa suffers by comparison. Brian Friel's memory play is set during that same summer of '36 in rural Donegal, with lower political stakes. Yet this dramatist, dubbed Ireland's Chekhov, is also remembering a lost way of life, encapsulated by a family of six siblings who are going to be shattered by industrialisation as well as by the divisive shedding of strict Catholic codes.

Michelle Fairley's Kate finds her prudish authority challenged by her more freewheeling sisters, and their brother, Finbar Lynch's Jack, is a lapsed missionary who has returned from Africa with a shameless admiration for the pagan festivities to which his houseboy introduced him.

Lynch is amusingly skew-whiff, retaining a stiff-backed pontifical manner while discombobulated by malaria, and all the sibling tensions are nicely focused in Anna Mackmin's intimate in-the-round staging – complete with kitchen sink and cast-iron stove, flagstones and encircling green grass.

There's one joyously wild moment when all five sisters whirl to Irish music on the wireless, and Niamh Cusack is particularly vibrant as the high-spirited, anxiety-suppressing Maggie. That said, having everyone address an invisible 10-year-old boy is awkward, and the romance between Andrea Corr's Chris and Jo Stone-Fewings's caddish Gerry is both gooey and grating. This production, though enjoyable, doesn't quite take off.

Lastly, Tim Supple's multicultural As You Like It proves a big disappointment after his bewitching Indian Midsummer Night's Dream. His young actors at the Leicester Curve are performing this one in English, with often clueless verse-speaking. The clown, Touchstone, can't even remember his gags. In fact, Supple has stripped Shakespeare's pastoral comedy of virtually all its wit.

Tracy Ifeachor rightly brings out a damaged and angry side to this heroine who's peculiarly excited by wrestling, but she subsequently lacks any charm, playing the moody dominatrix in her cross-dressed wooing games. Justin Avoth, though incisively intelligent, is encouraged to go over the top too, playing Jaques as a manic depressive who slathers himself in stag's blood.

Composer Nitin Sawhney and Ashwin Srinivasan's accompanying score features a haunting flute, like a woodland bird, but also an inordinate amount of mournful metallic twanging like mice blundering around inside a grand piano. Still, anything to drown out the dialogue, eh?

Burnt by the Sun (020-7452 3000) to 21 Apr; Dancing at Lughnasa (0870 060 6628) to 9 May; As You Like It (0116 242 3595) to 28 Mar