Give a child a loving, intact family and loving, intact extended family and you are about 95% there on the "normalcy," if by normalcy we mean raising a "whole" child or whatever the term is now called in the self-help section of the book store.
Georgie's got that.
As for raising the heir to the throne in a modern world, I suppose if I could offer any advice it's to just get on with things day to day. Don't lay awake nights worrying about what normal means (as it doesn't exist anyway).
The Queen did not have a "normal" existence. Sure, there's things she missed, but in the grand scheme of things, does it matter she never got on a line at the ice cream shop. She never watched her mom at the kitchen table fretting over money either. In some ways I think her grandmother Queen Mary was the best educator - telling her granddaughter she was an ordinary person who need not put on airs, but with an extraordinary place in the world. Embrace the extraordinary role and use it to try to make the world a better place than it was when you were born. I think Queen Mary got it right better than Diana, whose idea of "normalcy" was taking the boys to Disney where they got VIP treatment and went to the head of the line. Not to say Diana did not get some things right, most of her attempts at normalcy (visiting AIDS patients and going to Disney) were a bit grandiose. Again, trying to tell a child with an extraordinary role that they were "normal."