The six handwritten letters, sent to a favoured Buckingham Palace steward, sold for £15,100 at auction, exceeding the £2,300-£3,600 estimate.
One lot, which included a letter where Diana described Prince William’s adoration for younger brother Harry, was sold for £3,200 - around five times more than its estimate of £400-£600.
In the letter to Cyril Dickman, Diana wrote: “William adores his little brother and spends the entire time swamping Harry with an endless supply of hugs and kisses, hardly letting the parents near!
“The reaction to one tiny person’s birth has totally overwhelmed us and I can hardly breathe for the mass of flowers that are arriving here!”
In October 1992 Diana wrote to Mr Dickman ahead of a trip to Asia with the Prince of Wales: “The boys are well and enjoying boarding school a lot, although Harry is constantly in trouble!”
The lot containing the revealing letter sold for £2,400, more than double the £600-£900 estimate.
As well as divulging details about the private life of the young family at Kensington Palace, the messages from the 1980s and 90s show how fond Diana was of Mr Dickman, who provided her with support after the death of her father in 1992.
The six notes were part of a collection described as “the private letters between a trusted butler and the royal family”, which also included photos and Christmas cards.
John Foster, of Cheffins auctioneers in Cambridge, said interest in the collection had been “phenomenal”, with inquiries coming from as far afield as Japan, Australia and Canada.
He told the BBC: “One of the nice things about this collection is that it reveals the personal side. It’s not just thanking someone for an event, it’s things like the handwriting and the squiggly drawings.
“There is also mention of when Diana’s father passed away and how sad it was, talking of the children when they were at school, how much trouble they got into, just those personal touches which you never really get to hear about.”
Among the letters was a note appearing to wish Mr Dickman well on his retirement in 1992.
In it she wrote: “Cyril, you will be greatly missed by this particular Lady - thank you from the bottom of my heart for being so kind to me throughout the years and take great care of yourself, fondest love from Diana x.”
The six letters were part of a bigger collection which included other royal memorabilia.
One handwritten letter from the Queen sold for £1,500 - considerably more than the £50-£100 estimate.
In it, the Queen wrote: “Dear Cyril and Eva, I much appreciated your thoughts and sympathy on the death of my mother. We must all be thankful in the encouragement and pleasure she gave to so many during her long life. Elizabeth R.”
A boxed piece of cake from the Queen’s wedding in 1947 sold for £550.