I believe it is possible for a royal couple to have a modern family if they desire it. I think they will still be required to adhere to a certain amount of tradition due to their status, but they will be able to maintain a more modern family life. I believe royal couples in the past were more interested in maintaining the royal traditions than in having modern families. I believe things are changing with this newest generation.
I believe it is possible for a royal couple to have a modern family. It would seem that is exactly what William and Kate are trying to do in the United Kingdom. I find this pretty comforting given his history and the loss of his mother. All it takes is the will to live a common life.
It is not possible for a royal couple to have a modern family, and they shouldn't strive to be modern either. The whole reason we love royals so much is because they remind us of old times -- of fairytales and castles. And there is nothing more likely to burst that bubble than to think about a royal couple trying to emulate the average modern family.
Yes, this young royal couple in Great Britain is going to be more modern and Will and Kate will most likely do their best to give their children a more normal outlook and experience. But they are still going to be coddled and protected and photographed and know what their future will be so they are removed from contemporary experience.