I am the Kat that Walks By Itself

Have you read over the Potterverse essays at Red Hen Publications? I don't agree with the author about every little thing, but most of the arguments are very persuasive, in trying to illuminate and explain these (and many other) worldbuilding problems created by JKR's slapdash approach to characterization.

http://www.redhen-publications.com/potterverse.html

There's a whole list of subjects down the left-hand side; Dumbledore shows up in most of them, but there's a whole essay or two on him and his family as well.