Park Chan-wook is clearly in a very dark place. His head is bowed, his mood blue. What terrible circumstances could be troubling the South Korean director who masterminded the queasy excesses of Oldboy and the rest of his Vengeance trilogy? Recent incarceration by an unknown malefactor? Is he being hounded by a secret black-market organ-smuggling operation?

In fact, his cat has died, and he's still struggling to cope. "I'd had him for more than 10 years."

Mooka, Park's Russian Blue puss, was just one of the victims of a kitty reaper that stalked the set of his new film, Stoker. Composer Clint Mansell's mog died at the same time. "The only consolation is that it didn't happen during shooting, but during postproduction," says Park. The sumptuous Stoker is his first English-language production, but it's unmistakably his work: adorned everywhere with picturebook flourishes – harvestmen creeping over slim ankles, brushed hair dissolving into cornfields, blood-spattered foliage.

And a domestic void is at its heart, too: Mia Wasikowska stars as India Stoker, an 18-year-old girl mourning the death of her father in a car accident, unlike her mother Evelyn (Nicole Kidman), who seems liberated – especially when her husband's mysterious brother Charlie (Matthew Goode) appears at the funeral. No one with that orange a tan can be trustworthy, and India, with a certain icky fascination, is on the interloper's case. The name Uncle Charlie should ring a bell – another one, played by Joseph Cotton, turned up to upend a household in Alfred Hitchcock's 1943 film Shadow of a Doubt.

Park says he actually had to strip the script – originally written by Prison Break actor Wentworth Miller – of Hitchcock references; he has talked about the British director's influence on his work many times in the past, but he didn't want to tread directly in the legend's deep footsteps. Nor was Park especially inspired by the Nashville locations, or by the idea of making a film about America: the majority of the action takes place on the Stoker estate, from which he tried to expunge anything that would locate it in a particular region. It was the simple confined family drama that interested him, around which he could build his "gothic fairytale", filled with his own personal meanings.

"There's this element I brought into the film, this talk of wine," says Park of a loaded dinner-table scene, "There's a line where Evie appreciates how mature the wine is, and Charlie says: well, you can't compare it to a younger wine, which is too tannic. But we realise later on that he didn't pick the wine for Evie, but for India. When he pushes the wine to India and says: '1994: the year you were born.' And that was the year my daughter was born, so it was a nod to her."

Nicole Kidman and Mia Wasikowska in Stoker. Photograph: Sportsphoto/Allstar

Park made his 2006 romantic-comedy I'm a Cyborg, But That's OK because he wanted his daughter, Seo-woo, to be able to see one of his films – normally filled with vendettas, incest, extreme amateur dentistry and other frivolities. Stoker, down to its bat-winged title, is a step back towards his usual tormented idiom, so what message can its torrid coming-of-age story hold for his kid? Park, sat on the edge of the circle of lamplight, picking over a chocolate muffin, manicured nails tapering to sharp ovals, lets out a little chuckle. "I'm not the kind of director who aims to send a message out. But if you had to twist my arm, it would be: in knowing yourself, you can liberate yourself."

He leads by example. He agrees that he picked a script with identifiable Park traits as a way of cementing his "brand" as he makes a break, in his 50th year, for an international audience. There is something very self-aware and controlled about him in person: in a blue blazer, grey trousers, tortoiseshell glasses, cradling a leather-strapped Leica camera, he couldn't be trying any harder to channel the "classy cult-film dude" look. A former philosophy student heavily involved in the film clubs that sprang up, at the same time as the pro-democracy movements, at South Korean universities in the 80s, Park became a film critic while he was trying to ignite his directorial career. When no one reviewed his debut film, The Moon Is the Sun's Dream, he wrote a notice himself for the university paper under a pseudonym.

He has scary cinephile credentials, according to Hamish McAlpine, the former head of Tartan Films who unearthed Park for western audiences: "He's one of the brightest I've ever met. He's very versed in cinema – of the west, too. He once asked me if I had read a play by JM Barrie, Mary Rose; and I said no, my knowledge of him stopped at Lost Boys. Apparently, Barrie's estate refused Hitchcock the rights to film it. Park asked me if I could get him a copy [of the play]: probably 99.9% of western film scholars don't know about it."

With this depth of knowledge at his fingertips, Park became one of the directors at the forefront of the explosion in Korean cinema in the early noughties, notably with his massive local hit Joint Security Area, which agonised (like so many of the country's films) over the north-south rift. This year, the now-mature Korean industry reaches another waypoint, with three of its top directors making their English-language debuts. As well as Park, there's Kim Jee-woon, who brought Arnold Schwarzenegger and the zeitgeist back on speaking terms with the recent The Last Stand, and Bong Joon-ho, whose comic-book adaptation Snowpiercer, with its multinational cast, is one of the most awaited sci-fi projects of the year.

Park is acting as producer on Snowpiercer – not just for professional reasons, but as part of an obligation to Bong, who is seven years younger, integral to Korean society. "I'm not sure if you understand the importance of the junior-senior relationship in eastern culture," says Bong. "It's not exactly a mentor relationship. We've been friends and acquaintances for many years. He looked for me to finish the film in the right way. He'd often suggest ideas that needed quite a lot of money, not like a normal producer. He is a director as well, so he cannot suppress himself."

It's striking, though, that Park, Bong and Kim have gone down such different routes for their global breakouts, with self-avowed "control freak" Bong steering clear of Hollywood, and Kim (for Lionsgate) and Park (for Fox Searchlight) trying to make an accommodation with the studios. All three had to adjust to US-style sets, very different to the Asian system that places all authority in the director. But where Bong kept creative control, and Kim was essentially a hired gun on a star vehicle, only Park had to fight to preserve a personal vision with a studio – which eventually resulted in a 20-minute cut to Stoker to bring it in at a tidy 1hr 38min. "It's just such a different animal from what I've experienced in Korea," he says, "but it's just like how you can't really complain about the weather in the States when you're going over to shoot a film. The Searchlight people had good taste, though. There were some differences of opinion, but at least they didn't make any nonsensical remarks."

Perhaps calmness – not auteur strops – is the key to winning against the corporations. Park has plenty of it, but given the rancorous content of his work, you wonder what lies beneath the unrufflable exterior; McAlpine reckons he only ever opens up "after a few sakés". This composed quality is apparently something the director has always had. His childhood priest (he went to church every Sunday with his mother) told a teenaged Park that he make a good clergyman. "I'm guessing it was because of my manner," says Park, "Or maybe he thought I didn't like women; if he did, he was wrong – I like them so very much. But I couldn't bear the thought of going to a seminary, so that's when I stopped going to church. I realised: I go there as a habit, not because of any real belief."

And so we got Park for the devil's party. The stylised, deranged waltz through his Vengeance trilogy won him many western admirers, and the elegant – if increasingly overheated – Stoker puts him in good running for a lengthy international career (only Ang Lee and John Woo, among Asian directors, have managed it). Spike Lee's Oldboy remake, due later this year, should help. If it doesn't work out, then he has the family motto to fall back on – "Never mind!" – which Park has tried to impart to his daughter. He thought it up as his kiss-off to the obsessive, high-achieving rhetoric favoured by the old military regime: "It's a little more than 'never mind'. It's: if you're trying to do something, if it doesn't happen, don't fuss over it. You need to understand the Korean mindset to fully appreciate it."

Isn't Korea's most high-achieving modern director a bad example on this score? "Really? I don't think I've ever tried to make something happen that I've absolutely had to force. You know how they say: if you can't avoid it, enjoy it. For me, it's the other way around: if I can't enjoy it, I avoid it."