I promise, we'll get to Peter, though the fact that James named one of his sons for him is a start on things being different.
I think the Weasley parents are more old-fashioned, in a way. James is more of the, "Oh, my name's James" sort. Considerably younger than the Weasleys, after all -- he and Lily were only 20 or 21 when Harry and Neville would have been born.
Ahem... Lupin's been at Hogwarts for four years. He's definitely been Dora's classroom teacher. Of course, it may take a while (if it happens) for him to see her any other way.