Like posted earlier, there were periods of time when diana didn't speak to her mum, which would limit William and Harry's contact with her.
Moreover, Diana passed away young and their contact with their maternal relatives became lesser. Though you see pics of Lady Jane and Lady Sarah with the boys, they are very few.
The likelihood o them being in frequent contact with them is unlikely. Though of course as family in sure they never lost complete contact.
The reading could just be a duty expected out of him.