'I want to punch Adele in the face!" Kelly Clarkson throws back her head and guffaws. "She is just too good. I saw the Brit awards and I was bawlin' just watching her on YouTube, in a little box this big." We're talking about the dormant tradition of the confessional singer-songwriter in the pop charts, with Clarkson interspersing her thoughts with references to her "really rough upbringing". But off-the-cuff flippancies are never far away (though it turns out they're not so off the cuff – she uses the Adele line in other interviews later in the day). For someone who woke up at 1.30am in Germany, her capacity for exuberant chatter is remarkable.

As are many things about the course Clarkson has steered. She was the first winner of American Idol, before it became a defining juggernaut of a decade's pop culture; it's hard to imagine now, but when Clarkson first auditioned, the fate of the show – let alone its contestants – was an unknown. "I had no idea what the show was until the third audition," she says. "My goal was just to be a backup singer – I never intended to be in front. But then my apartment in LA burned down and I had to move home, I had no money and I had to sleep in my car for three days. I just auditioned for this thing that said they'd pay you, and it happened to be American Idol. I didn't go into it thinking this would happen; I went into it thinking it might pay my electric bill."

This is a point Clarkson emphasises throughout the interview: she has no interest in fame or celebrity, she never dreamed of being a star, she doesn't seek the limelight, she's just not that kind of girl. "Literally, my career is happenstance," she says, spreading her arms and with what sounds like astonishment in her voice. "I work very hard, but I always wonder how in the world I got here." Here, of course, is with four global multi-platinum albums, sell-out worldwide tours and a list of industry awards. And for all her bubbly charm, a steely professionalism glints occasionally. When asked to respond to Simon Cowell's recent comment that Clarkson "started to fight against what made her successful … one minute she wants to make pop records, and then she doesn't," she laughs loudly again, but there's a distinct flash of anger as she says: "Everyone's aware that My Life Would Suck Without You and Already Gone were huge pop hits, right? Just checking. Maybe someone should send 'em to him!"

Clarkson has the hardened industry songwriter's habit of describing her music as though arranging it in record shop genre categories: "My new single is very rhythmic pop-rock, and the next one is a little more dance, pop-rock, R&B; the album has a very fluid vibe to it, a little rhythmic, a little pop, a little rock, some singer-songwriter stuff on there, too." It's an underwhelming way to sell her album. So her protestations of ordinariness might all seem somewhat disingenuous – though it's refreshing to hear a pop megastar acknowledge concepts such as luck and chance, rather than grimly trotting out American dream cliches and Protestant work ethic myths – were it not for her own career decisions bearing it out.

Between promotional campaigns, she all but vanishes from the public eye, retreating to her homes in Nashville and Texas, where her family owns a 60-acre animal rescue ranch ("horses, goats, pigs, dogs; animals that are deaf, blind, mistreated, about to be put to sleep"). And famously, over the years, there have been the repeated clashes with her label. Reviewing her debut album, 2003's solid-but-unremarkable Thankful, Rolling Stone described her as "a pop posy whose career is tied for eternity to the whims of her American Idol overlords". During the subsequent eight years, the question of what sort of music it is appropriate for an Idol winner to record and release has been front and centre of Clarkson's career.

This came to a head in 2007 over the bleak My December, an album that opens with the girl who was meant to be America's sweetheart snarling " I hope the ring you gave to her turns her finger green" over grunge guitars, and ends with Irvine, a bare, flickering lightbulb of a ballad that sounds like a nervous breakdown in song form. Clarkson says she penned it alone in a hotel room, exhausted, at the "lowest point in my life". Too dark, too bitter, too negative; the reaction, both from label executives and, bizarrely, from critics who seemed to run with their line, was telling. It was possibly indicative that none of its critics had listened to Clarkson's previous album, Breakaway, particularly the song that would become its greatest success. Rolling her eyes, Clarkson laughs again. "My biggest song worldwide is Because of You, and … you may as well grab a knife. That song really is the most depressing one I've ever written. I tried to get it on Thankful, and was laughed at and told I wasn't a good writer. So then I tried to get it on Breakaway – and the label saw the results, people responding to it, and allowed it to become a single. Then took credit for its success, of course."

The episode also seemed to exemplify a sense that female anger no longer had the place in the mainstream that it had during the 1990s, when Clarkson was growing up listening to Alanis Morissette; she feels this is changing, raving about both Adele and country singer-songwriter Miranda Lambert's latest Pistol Annies project. "I looooove Pistol Annies!" she gushes. "Anything to do with harmonies, I love, and how bare is that production? Miranda is one of my favourites. Have I thought about collaborating with her? Uhhh – I might think about it every day! I run into her all the time and I swear to God she thinks I'm stalking her and she hates me. Every time I run into her, usually I'm intoxicated and I'm slurring, 'We need to sing a song!' at her. She says she wants to do it, but every time she has an album coming out, I do too, so we're both way too busy. Or she's just sidestepping me, I don't know, haha."

While Clarkson's fourth album, 2009's All I Ever Wanted, was a disappointment – from its brightly coloured artwork to its shiny production and its Katy Perry co-writes – it seemed to go out of its way to pretend that angry, rock Kelly no longer existed; that there was only happy, pop Kelly. But her new album, Stronger, seems free of such second-guessing. Almost every track kisses off someone or other; if it plays it safe in places, such as lead single Mr Know It All, then the cynical snarl of Let Me Down and the cast-iron pop choruses of What Doesn't Kill You and Einstein are full of the bravado and force that characterise Clarkson's best work. For once, she seems to be of one mind with her label. "This is the first record that my label and I have agreed on everything. There's one song that I was kinda, uh …" – Clarkson pauses delicately – "but it's not a bad song. I'm crossing my fingers that there's no more drama."

The drama, however, has been key to securing the loyalty of the global fanbase Clarkson never sought. She's a "ballsy, Texan, sarcastic asshole", as she puts it; her fight not to be moulded is now a key part of her public persona. But what she's fighting to retain is conventional and relatable – so much so that she sometimes seems like a fifth columnist in the oddball environment of the entertainment industry, particularly when she calls its bad behaviour out: blogging acerbically about Kanye West following his interruption of Taylor Swift's Video Music awards acceptance speech; revealing that songwriter Ryan Tedder gave the identical backing track to both her and Beyoncé without telling either, leading to uncomfortably similar songs winding up on both artists' albums; happily withholding sympathy when Perez Hilton was punched in the face by will.i.am's tour manager. Reminding her of each of these incidents sends Clarkson into more gales of laughter. "I come from a very hardcore sarcastic family, and if you can't hold your ground you need to shut up. And Perez had been dishing it out left and right – to people's children, 13-year-old-girls, putting stuff on their mouths in pictures. That's crass and gross. Recently, I heard he's changed. I don't know, I've never gone [to his site]. I don't believe in violence, but he was hateful."

One gets the impression that Clarkson's sense of self is hard won and highly prized. "I had to grow a thick skin from the age of five," she agrees, referring to a childhood defined by family breakdown and financial hardship. When Clarkson explains how, in contrast to "a lot of people who love to do these personas", she is just "constantly the same person", it sounds less like a dull lack of imagination and more like a triumph.

"I think I'm not unattainable," she reflects. "A lot of stars are, but you have a friend like me – I promise!" It is that promise that ensures, no matter how much Clarkson claims she would happily quit the industry if her records stopped selling, she is unlikely to have to do so for a long while yet.

Stronger is released on Monday on RCA