Speaking to Eugene Levy for the Canadian actor's TV travel show, the normally guarded British heir said he sometimes felt "overwhelmed" by family matters and vowed to keep his children safe from any excessive intrusion by the media.
"Worry or stress around the family side of things, that does overwhelm me quite a bit," the 43-year-old told the Schitt's Creek star.
"When it's to do with family and things like that, then that's where I start getting a bit overwhelmed - as I think most people would, because it's more personal."
Last year both Princess Catherine and the king, now 76, began treatment for cancer. While his wife is now in remission, William said it had been the hardest year he had ever had.
"Life is sent to test us," he said. "And it definitely can be challenging at times, and being able to overcome that is what makes us who we are. I'm so proud of my wife and my father, for how they've handled all of last year. My children have managed brilliantly as well."
William made his unusually candid remarks as he showed the actor around Windsor Castle, the royal home west of London where the king hosted US President Donald Trump in September. He also took Levy to a local pub.
There were light-hearted moments, with the prince saying he was a big fan of Levy's bawdy American Pie comedy films. But William also spoke about life as a royal and his vision for the future.
He touched on the intense press coverage of the break-up of the marriage of his father and his late mother, Princess Diana, saying the media had been "in everything, literally everywhere".
"The damage it can do to your family life is something that I vowed would never happen to my family," he said. "And so, I take a very strong line about where I think that line is, and those who overstep it, you know I'll fight against."
He said he did not think much about becoming king, but acknowledged that he planned to perform the role differently.
"I think it's safe to say that change is on my agenda. Change for good," he said. "That's the bit that excites me, the idea of being able to bring some change. Not overly radical change, but changes that I think need to happen."
The episode of The Reluctant Traveler With Eugene Levy featuring William is set to air on Apple TV+ on Friday.
