I wouldn't say that I hated the Dodds but as I read your post I realised that, on my recent reread, those were the parts I skipped too. I enjoy the interaction of the Dodds with the Marlows - the scenes at the breakfast table and, later, when we see them with Karen in their own home.

Peter's Room is my favourite book, I think but it's a close call with Falconer's Lure which IIRC was the first non-school story I read. I like Run Away Home but, as you say, for the character. I love the different reactions to the prospect of spending Christmas without Mrs Marlow and then to the proposed picnic on the beach. And, of course, the way they each deal with the Edward situation.

So, I think i'm saying that, for me, it's about character too.