The 65-minute documentary partly covers the Royal Family's struggle with media attention and includes footage of her approaching a paparazzo and asking him to stop taking photographs of the children while they were on a skiing holiday.
"If you are the Princess of Wales and you're a mother, I don't believe being chased by 30 guys on motorbikes who block your path, who spit at you, who shout at you and who react really badly to get a reaction from you, and make a woman cry in public to get the photographs, I don't believe that is appropriate," Prince William says.
"I sadly remember most of the time that she ever cried about anything was to do with press intrusion."
The documentary, which is called Diana: Our Mother, was commissioned by the Princes to remember Diana nearly 20 years after she died in a Paris car accident. It is the first time that the brothers have spoken so openly about the death of their mother in public. William talks of how he regrets how his last phone call with his mother was rushed and Harry speaks about how serving in the Army for ten years served as a release.
In another scene, Diana is shown struggling to enter a building due to the amount of photographers. William adds that his experiences of the press as a child have meant he has put up more barriers to them as an adult.
It also features interviews with some of Diana's closest friends, including Elton John, and survivors of landmine tragedies whom she had helped just before her death. The film discusses her royal wedding, international aid work and even the sale of her dresses to raise money for charity.
Diana: Our Mother is being broadcast on HBO at 10:00pm ET on Monday 24th July.