I think William & Harry knew their parents were going through a very tough time and was hurting but I think they knew their parents wouldn't do anything to purposely hurt them. Those early 90's weren't that pretty. It was a tough time for the family.
I don't think that Diana really grasped what would hurt her children. This is part of an article which writes about Diana's attitude prior to the interview. It relates to a section of Penny Junor's book.
Article
A 13-year-old schoolboy at the time, the young William watched the programme in the study of Andrew Gailey, his house master at Eton, says the book by Penny Junor.
Mr Gailey was said to have insisted that Diana explain face-to-face what she was about to do after learning about the BBC interview, and she eventually “reluctantly” agreed to go to the school.
The meeting lasted no longer than five minutes, during which she assured her son that the interview would “not contain anything controversial” and “would make him proud of her”, according to Junor.
But the young royal was said to have been left in disbelief by the succession of startling claims made by Diana – to an audience of 20 million people – including the revelation that: “There were three of us in this marriage.”
“Not unnaturally, he was deeply upset,” the new book says.
“By the time William emerged from Dr Gailey’s study, he was angry and incredulous,” it adds. “How, he must have asked himself, could his mother have done such a terrible thing?”
The revelations are published in the biography Prince William: Born To Be King: An Intimate Portrait
I have no idea if this is true but that can be said about everything that is written. But it seems to be in character. And she surely should have realised that the world would see the programme and her children would be hurt.