Coming into a meeting room on the 24th floor of a Manhattan skyscraper, the actor Alec Baldwin strides up to the wraparound windows, takes in the glorious 180-degree panorama and jokes, to no one in particular, “Ah! Yes! This can be my next apartment.” The 61-year-old lands his weight on a sofa and, taking out his phone, sitting extremely straight, nose almost touching the screen, he video-calls his wife Hilaria. “Look at this view I have of the city!” Baldwin cries, angling the camera for her. Quickly the couple are talking grocery needs, who missed whose call, which of their kids got bitten this morning during playtime at school.

“Bitten?” Baldwin repeats. “By who?”

As I’m sitting here anyway, I settle in and enjoy the spectacle: Alec Bloody Baldwin, in the wild. Today the actor has on a navy suit, his hair cut into a close steep wedge, the shape of a piece of cheese in a cartoon. Up close you realise what an awesome amount of time you’ve spent in this man’s company over the years, the large scored face and the half-hoarse Long Island burr the stuff of a thousand movies, TV episodes, comedy sketches and voice-overs.

By his own account, Baldwin has never been much good at saying no to work. Later on in our conversation he’ll tell me: “My schedule, 10 years ago especially? When I didn’t have a marriage at stake? I didn’t have kids at home? I just kept moving. I cut every ribbon. I would show up.” Baldwin will note that he has been in show business for 40 years, but his place in the culture is hard to define. He’s just… Alec Baldwin. Actor. Scourge of presidents and paparazzi. Voice of sports docs, Wes Anderson movies, Boss Baby, the machines in the Mission: Impossible films that threaten to self-destruct. In a coming movie – Motherless Brooklyn, a gumshoe caper directed by Edward Norton, out this month – such great faith is shown in the public’s intuitive recognition of Baldwin that for the first 15 minutes we are not shown his face, only the wide creased neck, those sloping Baloo-the-Bear shoulders.

‘It’s kind of a gallery of monsters. Where do they come from, this malignant class of public servant?: as Trump on Saturday Night Live. Photograph: NBC/Getty Images

On the sofa Baldwin is saying to his wife on the phone, “I think for legal reasons we don’t want you to say the name of the biter… Where am I? I’m here doing this interview. I’m here to meet, uh… Tom?” Still immaculately erect on the sofa, Baldwin swivels his eyes, Action Man-fashion, so that his gaze shifts past the phone. Oh! Me. I nod.

“I’m here to meet Tom. We’re going to talk about, uh… Hey. Tom. What are we gonna talk about?”

It’s a matter I’ve put some thought into. With Baldwin there’s just so much. Today I want to talk about the deep personal animosity that exists between this actor and the President of the United States. I want to whizz through a long career and get to the cool part, his unexpected late-career renaissance as a comedy player, first in Tina Fey’s sitcom 30 Rock and, afterwards, from 2016 to now, impersonating Donald Trump on Saturday Night Live. I want to talk about Baldwin’s first marriage to the actor Kim Basinger, and the daughter they had together, Ireland, who is now 24 and living in New York. I want to talk about Baldwin’s second marriage, to Hilaria Thomas, a former actor and yoga instructor, when he was in middle age and she was in her early 20s. I want to ask a difficult question, about what sort of personal reckoning is required, when you’re a man of Baldwin’s age and you’ve just had four young kids in quick succession.

Baldwin is waiting. I ramble something which he disregards, and he says to his wife, instead: “We’re gonna talk about you. How lucky I am to have you in my life. Look, when I’m done here I’m gonna run home quickly. I’m gonna try that. All right? I love you. Bye. Bye. Bye-bye-bye.”

‘The thought of her being out there and I don’t have her was unacceptable to me. I just had to marry her. I was so in love with her’: with his wife Hilaria, with whom he has four young children. Photograph: Lexie Moreland/Rex/Shutterstock

Baldwin hangs up and crosses his legs. Right! The interview. “I don’t have anything fresh to say in terms of Trump,” he warns right away. People always want to talk to Baldwin about the president, who he impersonates with real venom. He simply has Trump-fatigue, he explains, which cannot really be true because for a good long while Baldwin discourses, with brio, on his Nemesis-in-Chief. “Not only did I never dream a man like him would become president but, also, I didn’t imagine that he would be able to find so many like-minded people to come and serve him. It’s kind of a gallery of monsters, he has. Where do they come from, this malignant class of public servant?”

President Trump is also in Manhattan today, a few traffic-stuffed blocks away at the UN. Leaders from around the globe have travelled in for a summit, as has the young climate activist Greta Thunberg. I ask Baldwin what he makes of the Swedish teenager, her global constituency, on the whole, rather light on 61-year-old American males.

Oh, says Baldwin, he’s impressed, he’s impressed. He thinks the UN should hire Thunberg full-time or something. “I think we should have a young person who’s given some kind of a job. They’re given a title or they’re a liaison to the young community. And this girl? Great.”

His sketch-show impersonation aside, there is something gently Trumpian about Baldwin’s conversational manner. I have been told by those who’ve interviewed him before to expect eccentricity and entertainment, and an answer to one in every three or four questions. Often, Baldwin takes the gist of an enquiry and then, with echoes of Trump, launches into a startling impromptu flight.

‘She was kind of peaking. She was 37 and I was 32. We got married. We both were working all the time’: with Kim Bassinger in 1999. Photograph: Dave Lewis/Rex/Shutterstock

“I had a great plan once,” he says. “And I really mean this. I said to my wife, ‘Let’s liquidate everything we own! We have a house on Long Island. We have our apartment in Greenwich Village. Let’s sell everything. Convert it into cash. And we’ll stay in the most beautiful hotels around the world. One year in each city, during the kids’ childhood. We’re in Vienna, we’re in Tokyo, we’re in Cape Town. Rome, Paris, London. Moscow! Madrid!’ And my wife, she found it amusing. But said she would like the kids to go to school.”

Their kids are Carmen, six, and her three younger brothers, Rafael, four, Leonardo, three, and Romeo, one. The Baldwinitos, Hilaria calls them. “My wife and I, we’re like collectors,” Baldwin says. “Except that we collect our own children… I worry about my kids because they’re so loved. They’re so cared for. My kids get their ass kissed 24 hours a day by one of us.” (At time of interview, Hilaria was expecting their fifth child, but later revealed, in an emotional Instagram post, that she had suffered a miscarriage.)

In Motherless Brooklyn, Baldwin plays an intimidating industrial titan, loosely based on the New York infrastructure don Robert Moses. He is someone who raves, bullies and strong-arms, never seeming less than utterly furious. I see no signs of it during our conversation, through which Baldwin sits, mildly, with his hands folded across his lap, but this actor is popularly assumed to have a bit of a temper, too. He has lived 40 years in New York, a place where you feel the simmering fight instinct being kept in check by its citizens at all times.

There have been incidents. Baldwin was stopped in 2014 for riding his bike the wrong way on Fifth Avenue, and afterwards arrested for arguing with the cops. He was removed from a plane in 2011 after refusing to turn off his phone, a much-teased-about event that recently prompted his daughter Ireland to quip: “Why would you even start shit with the one place that’s still playing your movies?” Years earlier, when Ireland was about 11, Baldwin had left a mean-spirited message on her answerphone that later leaked to TMZ. He has been in at least two scraps with street photographers (1995, 2013) and there is a suit playing through the Manhattan courts, just now, resulting from a disagreement he had with a man over a parking space. Members of his young family were present for that one. I ask him: now that you’re the father of young boys, what do you tell them about confrontation?

Early breaks: in Knots Landing, which ran on TV from 1979 to 1993. Photograph: Kobal/Rex/Shutterstock

Baldwin takes the question in a playful spirit, and snorts. “My wife does a lot of that. My wife’s not taking any chances… You know,” he says, “I was not an aggressive person when I was a kid. I was little. Skinny. The third-string quarterback or whatever.”

Baldwin was born in 1958, on Long Island, an hour’s train ride from Manhattan, the eldest of four brothers (Daniel, William, Stephen), all of whom would go on to become actors, with different degrees of success. Their father, Alexander, was a war veteran turned teacher, supportive but strict. Baldwin told an anecdote, once, about his father biting his own hand during disagreements – better to stop him raising it. “He had dignity and integrity,” Baldwin tells me. “He wasn’t perfect, but he was a really good guy.”

Baldwin left Long Island in the mid-1970s, and in the early 80s he moved to Los Angeles, where he was cast as a heart-throb in Dallas spin-off Knots Landing. The actor recalls: “When I went to LA, my dad died. And I had that inclination, healthy or not, to replace him, this man who to me was like Abraham Lincoln in terms of his integrity. And I’m in Hollywood. Capital of integrity! Boy, that was a lonely time. It changed me and hardened me.”

Baldwin was 25. There were a couple of lost years when anything might have happened. “I drove around shit-faced for two years before I got smart,” he once said of a nascent drinking problem. He got sober at 27. A breakthrough Hollywood casting, as Jack Ryan in The Hunt for Red October, came aged 30.

Calling the shots: in Motherless Brooklyn in which he plays an ‘intimidating industrial titan’. Photograph: Glen Wilson/AP

At that time, Baldwin says, he was “obsessed with work. Trying to make it in the business and not getting that right, never getting that right. I married somebody who was successful. She was a very successful actress. Kim.”

Basinger. She had just been in Nadine and 9½ Weeks. “She was kind of peaking,” Baldwin recalls. “She was 37 and I was 32. We got married. We both were working all the time.” Their daughter Ireland was born in 1995. “She would go with Kim on location and I would go and meet them. Then we got divorced. There was a very acrimonious custody battle. Painful. Painful.”

What is Baldwin’s relationship with Ireland like now? “My relationship with my daughter is normal. Of course, it’s damaged as a result of high-conflict divorce. There are scars, there are echoes of that. It’s tough. But I get along great with my daughter.” Mostly, Baldwin says, “you look at all the time that was lost… If you did an analysis of the actual days I spent with Ireland [when she was growing up], you’d be appalled at how little it was.”

Baldwin recently took part in a charity “roast” for a cable network – a feature-length TV savaging, something like This is Your Life, only researched and written by Satan. A panel of comedians had great fun teasing Baldwin’s reputation for absentee parenting. And then, midway through, as a surprise, his daughter walked out to make a speech of her own. “Hi dad,” it began, “I’m Ireland.”

The Baldwin boys: with brothers William, Stephen and Daniel. Photograph: Jason LaVeris/FilmMagic

When Baldwin left Ireland that angry voicemail message, in the mid 00s, his reputation took a heavy blow. On the charity roast they piled on this and other mistakes with glee. I ask Baldwin why he ever agreed to this. “It was unbearable,” he says, helplessly, but it raised a lot of money – $1m, he claims. He hated the experience from the get-go. He only wanted to finish and go home.

In 2011, Baldwin was coming to the end of a long run on 30 Rock. That sitcom, about a comedy writer (Fey) and her dealings with a misanthropic TV exec (Baldwin), revived his reputation and his career. “I mean, we won every award three or four times.” He was as successful as he’d ever been, but he was lonely. When he met Hilaria at a restaurant, “it was incontrovertible. The thought of her being out there and I don’t have her was unacceptable to me. I just had to marry Hilaria. I was so in love with her. It was somebody who I thought: ‘I am intrigued by, I am fed by, I am buoyed by…’ There were a lot of other guys she could have married who were age-appropriate. It happened quickly. I met her in February. I moved in in November. We got married the following June.”

What did Baldwin’s friends make of it all? The speed? The corking age difference? “I think it was understood that I was hungry to be a father again. And [this time] I wanted to know these people. I wanted to watch human development in real time… I wanted a family,” Baldwin shrugs, “and boy! Do we have one.”

On that charity roast for cable, the most savage joke made at his expense was also the saddest; a joke, like all the best comedy, that was underpinned by basic human truth. “The good thing about having kids late in life?” one panellist said. “Young, strong pall-bearers.”

When I mention this, I’m not sure how Baldwin will react. His response is unexpectedly tender. Conversation with him is a little like riding a marine animal. You hold on. You laugh and gulp down water. You abandon, completely, efforts at navigation. Now he speaks softly. “It’s frustrating. I sit there, with some regularity, driving in a car, or whenever I have a moment to breathe. And I sit there and I think: ‘You know what? I wish I had more time.’”

Baldwin continues: “There’s drawbacks to my kids, me being this age. But there are benefits, too. I’m there. I’ve made them a priority. It’s made me much more mindful: ‘How do I make the most of my time with them?’” He uncrosses and recrosses his legs. He’s speaking so quietly I have to lean forward to hear him clearly.

“You know, sometimes I sniff my kids.”

At first I don’t catch this. I have to ask him to repeat himself.

“I huff them,” Baldwin explains. “You know, like people would huff chemicals.”

There is something so unbearable about this image that I have to sit back on the sofa for a moment. Baldwin is a talented, capricious, occasionally ridiculous man. In this moment he only looks like a sad soft toy. “Ten extra years!” he says. “I wish I had 10 extra years! I wish I was 50. But, y’know, life. There is no pause button. There is no reverse button.”

Baldwin checks his watch. He has to go, across town to another meeting and then home, to Hilaria and the Baldwinitos. “There’s, like, a sacred part of the day,” he explains, “between 5pm and 7pm, when we don’t do anything but be with the kids. Feed them. Bathe them. It takes time. There’s so many of them… Which sounds insane, right? It is insane. Let’s face it. It’s insane.”

Baldwin is rubbing his head, but for all his talk of insanity he appears delighted, and when he strides from the room it’s with a vast, cartoony smile on his face, those sloped shoulders and that wedge of hair weaving out the door, towards the lifts, as he moves against the clock.

Motherless Brooklyn is in cinemas from 6 December