Richard III did
not have the appearance of an egg, in fact there is no evidence of him having been deformed in any way - that's all Tudor
propaganda, immortalized by
The Bard who was writing, don't forget, for a
Tudor queen.
As for the princes in the tower, yet again there is nothing more concrete than legend to link their deaths with Richard III, and the years of violence and bloodshed - well, yes, being as it was all during the War of the Roses, to which the succession of the Tudors finally brought an end. D'uh!
As for the nursery rhyme itself, wasn't it written by Louis Carroll? In parody of indecisive politicians or something?