Maurice Sendak looks like one of his own creations: beady eyes, pointy eyebrows, the odd monsterish tuft of hair and a reputation for fierceness that makes you tip-toe up the path of his beautiful house in Connecticut like a child in a fairytale. Sendak has lived here for 40 years – until recently with his partner Eugene, who died in 2007; and now alone with his dog, Herman (after Melville), a large alsatian who barges to the door to greet us. "He's German," says Sendak, getting up from the table where he is doing a jigsaw puzzle of a monster from his most famous book, Where the Wild Things Are. Sotto voce, he adds: "He doesn't know I'm Jewish."

At 83, Sendak is still enraged by almost everything that crosses his landscape. In the first 10 minutes of our meeting, he gets through:

Ebooks: "I hate them. It's like making believe there's another kind of sex. There isn't another kind of sex. There isn't another kind of book! A book is a book is a book."

New York: "You get pushed and harassed and people grope you. It's too tumultuous, it's too crazy!"

The American right: "These Republican schnooks would be comical if they weren't not funny."

Rupert Murdoch: "His name should be what everything is called now." But he publishes you! "Yes! Harpers. He owns Harpers and I guess the rest of the world, too. He represents how bad things have become. But I don't know a better house. They're all in trouble. They're all terrible."

Sendak shakes his head beneath the low-beamed ceiling, in this room full of art and old rugs. "I can't believe I've turned into a typical old man. I can't believe it." He smiles and his face transforms. "I was young just minutes ago."

To his millions of readers, of course, Sendak will always be young, a proxy for Max in Where the Wild Things Are, who runs away from his mother's anger into the consoling realm of his own imagination. There are monsters in there, but Max faces them down before returning to his mother for reconciliation and dinner. Sendak's own exile took rather longer to resolve. The monsters from Wild Things were based on his own relatives. They would visit his house in Brooklyn when he was growing up ("All crazy – crazy faces and wild eyes") and pinch his cheeks until they were red. Looking back, he sees how desperate they all were, these first-generation immigrants from Poland, with no English, no education and, although they didn't know it in 1930, a family back home facing extinction in the concentration camps. At the time, all he saw was grotesques.

That included his parents. If he had come from a happy home, says Sendak, he would never have become an artist, at least not the kind of artist he is. Sendak's picture books acknowledge the terrors of childhood, how vicious and lonely it can be. In his latest book, Bumble-Ardy, the hero is a piglet who loses his neglectful parents to a slicing machine on the first page and is left in the care of an aunt. When Bumble turns nine, she throws him his first ever birthday party and, in the manner of most Sendak stories, things take a dark turn: older pigs gatecrash and, in a kind of porcine burlesque, wreck the place. The pictures are feverish and transporting – and, although the book ends in forgiveness and a hug between aunt and nephew, the sense of precariousness around Bumble remains. "I refuse to lie to children," says Sendak. "I refuse to cater to the bullshit of innocence."

Things take a dark turn … Bumble-Ardy

The darkness of his childhood flowed down from his parents. Sendak's mother was sent to the US from Poland when she was just 16, alone but for the name of someone she could rent a room from. She was sent, says her son, because her own mother "couldn't bear her any more". Sendak's mother had been a flirt and a trouble-maker, who had "committed herself to every living human male in the village", including Sendak's father, the son of a rabbi. "He had prestige and was extremely handsome and devil-may-care. He came here after her and became a drudge. His family was sitting shiva for him back in the old country because he had done this terrible thing, chasing a girl when your father is a rabbi and schlepping all the way to New York."

It still gives Sendak vertigo to consider the improbability of his parents' survival. For years, he would look at their photo albums and wonder about these people, their families. "The shock of thinking I would never know them was terrible. Who were they?"

He says: "Dead people."

Then: "This is true. My father belonged to a Jewish social club. The day of my barmitzvah he got word [through the club] that he had, no longer, a family. Everyone was gone. And he laid down in bed. I remember this so vividly. And my mother said to me, 'Papa can't come.' And I was having the big party at the colonial club, the old mansion in Brooklyn. And I said, 'How can Papa not come to my barmitzvah?' And I screamed at him, 'You gotta get up, you gotta get up!' And of course he did. And the only thing I remember is looking at him when the guests burst into For He's a Jolly Good Fellow. And my father's face was vivid, livid, and I knew I had done something very bad, that I had made him suffer more than he had to. This 13-year-old ersatz man."

They were traumatised people, his parents, angry, fierce, "nuts", and understandably so. In such fires Sendak's talent was forged. "And then you grow up and you do books for children."

He is still raging. But since Eugene's death, says Sendak, it is merely an echo of his former anger. He looks around his property, built in 1791 and boasting in its grounds one of the last elms still standing in Connecticut, and approaches something like peace. He knows he is lucky and has been lucky for a long time. His relationship with Eugene, who was a psychoanalyst, lasted almost 50 years. His parents never knew – not officially. "Of course, they knew. Especially my father. My mother was so bewildering and strange and lived in another world, I don't know what she knew. Nothing was said, but if something had been said, I would have been thrown out of the house. And yet they met him and respected him. Strange."

Is it any wonder, he says, that his work pitches against euphemism and whitewash in favour of the unvarnished truth? It was a cousin who first encouraged Sendak to look beyond his narrow life in Brooklyn. She was a communist and they weren't supposed to associate with her, but he and his sister would sneak off to see this woman, who recognised his talent for drawing. He had always hated school and, to his parents' horror, eschewed university to become a commercial illustrator. His first job, in 1947, was illustrating a physics text book called Atomics for the Millions. Since then he has illustrated more than 100 books, and written and illustrated more than 20. Where The Wild Things Are, published in 1963, has sold more than 17m copies, but it is not his favourite. That honour goes to Outside Over There, about siblings. Sendak was very fond of his siblings.

'Why were we so unkind?'

The term "children's illustrator" annoys him, since it seems to belittle his talent. "I have to accept my role. I will never kill myself like Vincent Van Gogh. Nor will I paint beautiful water lilies like Monet. I can't do that. I'm in the idiot role of being a kiddie book person." He and Eugene never considered bringing up children themselves, he says. He's sure he would have messed it up. His brother felt the same way: after their childhood, they were too dysfunctional. "They led desperate lives," he says of his parents. "They should have been crazy. And we – making fun of them. I remember when my brother was dying, he looked at me and his eyes were all teary. And he said, 'Why were we so unkind to Mama?' And I said, 'Don't do that. We were kids, we didn't understand. We didn't know she was crazy.'"

There was a partial reconciliation with his parents, a moment of understanding. They never made much of his work except once, when he was asked to illustrate a set of stories by Isaac Bashevis Singer, winner of the Nobel prize for literature in 1978. They were proud of that, he says. For the illustrations, Sendak went back to the family album. "There were the photographs my father had of his younger brothers, all handsome and interesting-looking, and the women with long hair and flowers. And I went through the album and picked some of my mother's relatives and some of my father's and drew them very acutely. And they cried. And I cried. So there was that. And there still is that."

To die like William Blake

He's crazy, too, he says. "I'm totally crazy, I know that. I don't say that to be a smartass, but I know that that's the very essence of what makes my work good. And I know my work is good. Not everybody likes it, that's fine. I don't do it for everybody. Or anybody. I do it because I can't not do it." You can't be that crazy, I say: you managed to stay in one relationship for half a century. "Yes! And he was – well. He was a man who loved music and reading. He never smoked and he died of lung cancer, utterly ridiculous. I had that friendship for a long, long time."

Not long after Eugene died, Sendak started having heart trouble. He just "caved in" with sadness, he says. Every week, he loses more of his friends. Just last week a great pal died, a publisher in Zurich. "It accommodates us older people to the inevitability," he says. "I just miss them, terribly. It's no fun being lonely."

But he has the dog, whose great head he likes to put his arms around and nuzzle – and Lynn, who comes to look after him. In spite of his kvetching, he says, when it really comes down to it, "I'm a lucky buck." He is working on another book, about noses. He listens to Schubert, "a darling boy", and his hero Mozart. And he is returning to those authors he wants to reread before he dies: Samuel Palmer, Proust, George Eliot. He loves Middlemarch, although "Daniel Deronda, oy gevalt! She put aside her hard hat and was determined to be sweet and understanding. That won't get you anywhere, honey."

And with that he's off again. Of Salman Rushdie, who once gave him a terrible review in the New York Times, he says: "That flaccid fuckhead. He was detestable. I called up the Ayatollah, nobody knows that." Roald Dahl: "The cruelty in his books is off-putting. Scary guy. I know he's very popular but what's nice about this guy? He's dead, that's what's nice about him." Stephen King: "Bullshit." Gwyneth Paltrow: "I can't stand her."

He looks fleetingly sheepish. "Look, life is pretty dreadful most of the time. Even in the country that's so pretty with the flowers and leaves and sunshine. And I was abandoned when he died! I'm alone. I feel like an old bubba. And I'm not kind all of the time, I'm not nice all the time."

Sendak is in search of what he calls a "yummy death". William Blake set the standard, jumping up from his death bed at the last minute to start singing. "A happy death," says Sendak. "It can be done." He lifts his eyebrows to two peaks. "If you're William Blake and totally crazy."

• This article was amended on 4 October 2011 because it said: "Sendak's picture books acknowledge the terrors of childhood, how viscous and lonely it can be."

• Bumble-Ardy, published by HarperCollins, is out now price £12.99.