What about
Rosamund or
Rosalind nn
Rose/
Rosie? Those seem formal enough for a royal first name. I like
Eleanor,
Charlotte and
Alice.
Diana could be a mn, and
Elizabeth could be there, since most of the females seem to have it as one of their mns (
Anne,
Beatrice,
Zara, and
Louise), but a Scottish form would be nice.
Boys-
Arthur as a mn only, it's too corny/ too much to live up to as a fn. Personally, I'd stay away from the names of living relatives (
Charles,
Edward,
James), but
Phillip would be fine, since that's great-grandpa, and after this summer, I wouldn't be surprised to hear that he died in his sleep.