The band’s back together. Alfred Molina plays Rothko for the third time in Michael Grandage’s revisiting of John Logan’s richly textured two-hander, first seen at the Donmar in 2009 and then bypassing the West End for Broadway.

Back by feverishly popular demand, Jim Steinman’s mega-musical is no longer in danger of alarming unsuspecting opera-goers. A year on from its Coliseum debut, this indisputably bonkers show moves to the West End venue it was surely always destined for – that lingeringly inhabited by its rock operatic forebear.

It is, perhaps, a tale that suffers from overfamiliarity. Tina Turner’s rags-to-riches story – from humble beginnings as little Anna Mae Bullock in Nutbush, Tennessee, to her discovery, reinvention and sickening abuse by husband and manager Ike Turner, and finally her rebirth as a solo rock'n'roll star – is the stuff of showbiz legend.

You could be forgiven for not remembering the “coughing major” brouhaha in 2001, coming as it did the day before 9/11, when we had rather more pressing matters to attend to than a contestant being accused of cheating on television quiz show. But playwright James Graham has mined an entertaining confection from the affair and its subsequent court case in 2003.

Whatever the weather, this week is Frozen. On Broadway, the Disney musical of that name begins previews, but let’s let that go. In the West End, our Frozen has no Elsa, no Anna and no glittery gowns. Although it does have plenty of ice imagery. No, our Frozen is a much darker story; it’s a revival of Bryony Lavery’s 1998 award-winning play about a child killer – definitely no singing, no dancing, no hummable tunes.

Eugene O’Neill’s 1945 play Long Day’s Journey Into Night is famously a portrayal of the hellish damage that a sick person can wreak on their family, closely based on his own family. Mary and James Tyrone are images of his own parents, down to details like the father’s compromised acting career, the mother’s post-natal suffering from her last childbirth and subsequent addiction to morphine, and of course the emotional havoc for the small sons when they discover their mother’s affliction.

Casting decisions do not usually make gripping theatre. But in Robert Icke’s version of Friedrich Schiller’s 1800 political thriller, newly transferred from the Almeida to the West End, settling the question of which of two actresses will play the title role and which her nemesis, Elizabeth I, is an edge-of-the-seat moment night after night. Heads or tails? Before the entire assembled cast, the spin of a coin (a sovereign, of course) decides it. And with the result shown on screens that flank the stage, the audience is the first to know.

At Wednesday’s matinée, Lia Williams loses the call (pictured below), and in a blink the supporting cast have dropped to one knee in reverence to her opposite, Juliet Stevenson. The removal of Williams from the stage – brutally stripped of her jacket and shoes – follows swiftly. At the point the play begins, Mary has already spent 19 years as a prisoner, incarcerated at bleak Fotheringay Castle for fear that she will lead a Catholic revolt and usurp the English throne.That silver sovereign isn’t just a useful way of keeping the production fresh and the cast on its toes. It’s also a metaphor for Schiller’s treatment of these two remarkable figures from history. Despite their obvious differences – Catholic/Protestant, four-times-married/virgin queen – the play reveals them to be two sides of the same coin.

Icke’s production amplifies this by giving them identical mannish haircuts and velvet trouser suits. Both have to fight to hold their own in a man’s world. Both are passionate, intelligent, acutely aware of the random accidents of birth that placed them at opposite poles on the political spectrum, yet which also made them kin. One is imprisoned by high walls, the other by royal status, “a prison cell with jewels”. Thanks to the alternating casting, they conceivably are, in Mary’s words, “sister queens” who intimately know each other’s minds.

Yet, as an account of events as they happened, Schiller’s text is unlikely to help anyone pass their History GCSE. Not only does he use speculative gossip as a key engine of the plot (the Earl of Leicester’s romantic entanglement with both queens, no less), but he imagines a major event that certainly did not happen. Yet so brilliantly does he dramatise the fanciful face-to-face encounter between the two women that a poetic truth emerges.

The same might be said of the added tissues of fiction in Icke’s production, which is very much a “version” rather than a translation. In the moments before her execution, as Mary prepares to meet her maker, she receives the last rites from a secretly ordained priest – here played a woman. Icke clearly wanted to contrast the warm, female support around the doomed but radiantly resigned Mary with the chilly male courtiers who leave Elizabeth high and dry to bear the guilt of regicide. A female priest is surely no more unlikely a sight on a London stage than an Afro-Caribbean courtier, yet interestingly it triggered what sounded like barely stifled disbelief around the stalls.

Elsewhere, too, Icke finds contemporary resonance in spades. Just because a thing is popular, does that make it right? This is the crux of Elizabeth’s dilemma. The duplicity and back-stabbing among Elizabeth’s courtiers are pretty familiar too. Icke has one of them describe another’s actions as “flip-flopping” to drive home the point.

While it’s easy to laud the female leads in this production – Stevenson and Williams are equally affecting in their steel and vulnerability – it’s harder to love the supporting men (roughly half of them new to this transfer). Trussing them in tight-fitting, single-buttoned suits gives them a physical awkardness that is almost certainly intended. In Elizabeth’s day, of course, they would have vied with each other to sport the most flamboyant cuff or ruff. Instead, that rivalry shows itself in oily manners and a nervy awareness, every time each of them opens his mouth in Elizabeth’s presence, that it could either make or break him.

Elliot Levey (new to the cast, pictured above) is superb as Elizabeth’s advisor-in-chief Lord Burleigh, a man who cloaks his hatred of Catholics in seeming reasonableness, and whose cocky “I know more than I’m telling” rise of the eyebrow on every exit becomes increasingly chilling. John Light grows convincingly frantic as his own multiply double-crossing plots begin to ensnare him, while by contrast Michael Byrne’s ancient Yorkshireman Lord Talbot is a lone voice of genuine kindness in Elizabeth’s ear.

Hildegard Bechtler’s bare set has transferred well, its doubled curve of brick castle wall looking suitably permanent and stark at the Duke of York’s – you almost feel its winter chill. Yet the extravagant closing sight of Gloriana in her pomp is just as savage. This is a piece of theatre that lets no one off lightly. Even Paul Arditti’s sound design, a persistent low hum of tone clusters, seems designed to make you ultimately want to howl.

• Mary Stuart at the Duke of York's Theatre until 31 March

• Read the review of the original Almeida production, which covers both sets of performances from a matinee and an evening perspective
• Read more theatre reviews on theartsdesk

Overleaf: Robert Icke's dazzling career so far