Also in attendance were the queen's youngest son, Prince Edward, with his wife Sophie and their children, and Princess Eugenie, the daughter of Prince Andrew.
In 2018, Commonwealth leaders had agreed that Prince Charles would succeed Queen Elizabeth II as the head of the Commonwealth in an honorary, non-hereditary position.
William, second in line to the throne, made the comments while addressing a dinner in Kingston, Jamaica’s capital.
Speaking on Apple's 'Time to Walk' podcast, the 39-year-old Duke of Cambridge reflected upon the royal family's love of long walks as well as the life lessons he has picked up over the years.
"And my mother, she'd be driving along, singing at the top of her voice. And we'd even get the policeman in the car, he'd be occasionally singing along, as well," Prince William said.
The show, presented by Indian-origin BBC journalist Amol Rajan, alluded to royal sources speaking to journalists behind the scenes.
There is no word on whether Princess Diana's death will be depicted on the show, but the casting suggests viewers will certainly see events leading up to and possibly following the crash.
Prince Charles, his wife Camilla, Prince William and his wife Kate the Duchess of Cambridge made a rare joint appearance at the premiere.
Vinisha Umashankar, a 14-year-old girl from Tiruvannamalai, has featured among 15 finalists for the first-ever Earthshot Prize, launched by Britain’s Prince William last year.
Harry was best man at William's wedding to Kate Middleton in 2011, and the announcement comes after the birth of William and Kate's third child on Monday.
Kate, the wife of Britain's Prince William, has given birth to a baby son, Kensington Palace announced Monday.