Donald Trump Jr. is the Trump who has not always seemed at ease with being a Trump. He grew up in the penthouse of Trump Tower but was happy to escape the gilded trappings of his Manhattan childhood to spend parts of the summers hunting and fishing with his maternal grandfather in the woods of what was then Czechoslovakia.

After graduating from his father’s alma mater, the Wharton School at the University of Pennsylvania, he tended bar in Aspen, Colo., rather than immediately join the family business. Several months later, on Feb. 25, 2001, during a Mardi Gras celebration in New Orleans, he was arrested on charges of public drunkenness and spent 11 hours in jail.

“I think, like anyone else, I made my mistakes,” Mr. Trump said of his arrest. “We have to be honest with ourselves. I’m not good at it, moderation. You have to have the conversation, be a realist, and say, ‘I guess I’m not doing myself any favors.’”

In 2001, Mr. Trump, the eldest of the five children from Donald J. Trump’s three marriages, went to work for the Trump Organization in the same building where he had grown up. He rose to executive vice president, and his status as a family member in good standing was on display when he appeared as a boardroom adviser on “The Apprentice,” the NBC reality show that re-established his father as a celebrity mogul nearly two decades after he had captured the public’s attention with his first best seller, “The Art of the Deal.”