"My entire family has blond and curly hair."
Translation:Toute ma famille a les cheveux blonds et frisés.
You're right. It's really better. But nevertheless there is absolutely no reason to reject "Ma famille entière". No reason at all.
If Duolingo wants us to write "Toute ma famille...", he just has to propose "My whole family". A little consistency can't hurt...
You were probably not necessarily specifying each and every specific hair on their heads so there is probably some latitude to discuss non-specific hairs.
Whereas if you were discussing a nose or a chin or even an arm then you really have no choice but to be specific.
Unless of course, you want to say that she broke an arm (elle s'est cassé un bras) as opposed to she broke her arm (elle s'est cassé le bras).