Well, I doubt it's in the Oxford English Dictionary but I'd class Rose and Donna as chavy.
Nope, to be a true chav is a lifestyle choice, not a background upbringing as the tabloids would have us believe - and the main aspect of choosing chavness is choosing *not* to develop, *not* to improve onesself.
Since both Rose and Donna are very to go places, learn new stuff and generally improve themselves and their lot in life, that'd be the exact opposite of being a chav.
Their mothers, OTOH, are a different matter. (And, yes, Sylvia Noble in particular is meant to be middle-class, but she wants to stagnate, and Donna to stagnate, and that makes her a chav, IMO...)