Diana came from a most appallingly dysfunctional family, and the fact that this was not recognised by the RF suggests to me that this sort of dysfunction was considered normal in hoity toity circles.
I can imagine that, having been deprived of a day to day relationship with her own mother from a young age because of her father's vindictive pig headedness, she was deeply affected on a personal level by the experience of being sidelined by a nanny when she herself divorced.
I suspect she also realised once divorced that the Establishment was going to freeze her out (as happened to Fergie) and was determined to keep a foot in the game, so to speak, by making her position as mother of her royal sons unassailable.