At age 81, with over four decades of dealmaking and corporate cage-rattling under his belt, Nelson Peltz would seem to have pretty much everything.

He’s a billionaire. Until the hedge fund billionaire Ken Griffin came to Palm Beach, Fla., Mr. Peltz had the largest property tax bill in town, with an oceanfront estate estimated to be worth $334 million.

His 130-acre property in Bedford, N.Y., known as High Winds, has its own helipad, indoor ice rink and waterfall. He has use of his company’s jet. (But so far, he owns no yacht — he rents one instead.)

He also has an undeniably full life apart from his business: He has two children from his first marriage.

He also has eight children (including two sets of twins) with his wife since 1981, the former model Claudia Heffner.

His eldest child from that marriage, Matt, is a partner and co-chief investment officer at Mr. Peltz’s Trian Partners.

At age 81, with over four decades of dealmaking and corporate cage-rattling under his belt, Nelson Peltz would seem to have pretty much everything.

He’s a billionaire. Until the hedge fund billionaire Ken Griffin came to Palm Beach, Fla., Mr. Peltz had the largest property tax bill in town, with an oceanfront estate estimated to be worth $334 million. His 130-acre property in Bedford, N.Y., known as High Winds, has its own helipad, indoor ice rink and waterfall. He has use of his company’s jet. (But so far, he owns no yacht — he rents one instead.)

He also has an undeniably full life apart from his business: He has two children from his first marriage. He also has eight children (including two sets of twins) with his wife since 1981, the former model Claudia Heffner. His eldest child from that marriage, Matt, is a partner and co-chief investment officer at Mr. Peltz’s Trian Partners.

His photogenic younger children have thrust him into the tabloids and onto the Hollywood red carpet. Nicola, an actress (“Bates Motel,” “Transformers: Age of Extinction,” “Welcome to Chippendales”), married Brooklyn Beckham, son of David and Victoria Beckham, in a splashy wedding at the Peltz Palm Beach estate in 2022. Will is also an actor (“Unfriended,” “Euphoria,” “Manifest”). Brad played hockey for Yale and was drafted by the Ottawa Senators.

And yet Mr. Peltz yearns for something that continues to elude him: the respect from the corporate elite, which he craves and feels he deserves. Could admittance to the inner sanctum of one of the best-known and most respected companies in the world — the Walt Disney Company — deliver that?

On and off for almost a year and a half, Trian Partners has waged an intense corporate fight by controlling a $3.5 billion stake in Disney and pushing for two board seats and influence over the company’s strategy. Mr. Peltz’s ammunition is a barrage of criticism of Disney’s management and board: The stock has plunged; costs have spiraled out of control; a string of big-budget film flops has raised questions about the company’s creative engine — problems that Mr. Peltz says he can reverse with his operational skills and strategic insight. While he concedes he has no experience in entertainment, his opinions, he says, are informed by his children and their high-powered friends, including Elon Musk, who has been critical of Disney.

The proxy battle has pitted him against Disney’s chief executive, Robert A. Iger, one of the media industry’s most powerful executives and someone Mr. Peltz once considered a good friend. Mr. Iger and Disney’s board have pushed back hard, even enlisting the support of the Disney family, including Abigail Disney, who has long complained about Mr. Iger’s lofty compensation. The increasingly bitter contest is hurtling toward a climax on April 3, when Disney will hold its annual shareholder meeting and proxy votes will be counted.

That this fight is over far more than a couple of board seats, or even a multibillion-dollar stake in the company, was abundantly clear in a series of interviews with The New York Times at Trian’s offices on Park Avenue and in Palm Beach, and over the phone.

During the interviews, Mr. Peltz — who has had numerous similar run-ins with corporate giants such as Procter & Gamble, Heinz and Unilever — repeatedly lamented his reputation as a provocateur and “activist” investor, a thorn in the side of chief executives and their boards.

He hates being mentioned in the same company as a rogues’ gallery of activists, buyout operators and corporate raiders, as he often is. He thinks he should be compared to someone he admires and tries to emulate: Warren E. Buffett.

“Does Nelson feel misunderstood? He probably does,” said Arthur Winkleblack, who was chief financial officer at Heinz when Mr. Peltz waged a successful proxy contest there in 2006 and joined the board. “Not all activists are the same. There are activists who are not nice people. There are activists who are.”

Whatever label is attached to him, there’s little chance that Mr. Peltz will be embraced by the august members of the Business Roundtable, the Washington-based lobbying group of elite chief executives, given his long track record of public criticism of boards and chief executives, and his efforts, when rebuffed, to elbow his way into America’s boardrooms.

Jamie Dimon, the chief executive of JPMorgan Chase and a former chairman of the roundtable, recently came out against Mr. Peltz in the Disney proxy fight, citing the disruption that activist investors can bring to a board. JPMorgan is advising the company in its proxy defense. Disney has paid JPMorgan over $160 million in fees since 2014 as a client, according to LSEG, a financial data provider.

One measure of Mr. Peltz’s continuing notoriety is the reluctance of many people who have worked with him to speak on the record — even people he counts as friends and admirers, some of whom he recommended The Times interview for this article. That’s especially true in the midst of the Disney fight; several people said they didn’t want to be caught in the crossfire between Mr. Peltz and Mr. Iger, let alone Mr. Dimon. Both chief executives cast long shadows in the entertainment and business worlds.

“He’s like the uninvited guest who crashes a dinner party,” said Charles Elson, a former director of the John L. Weinberg Center for Corporate Governance at the University of Delaware. “No matter how charming, he’s not going to be welcome.”