Is it possible to have 2 separate email lists in one Yahoo group?

Question

Or somehow designate email addresses into separate categories, ie, "family" or "friends"

Answer 1

No not really.  You can use the facility to receive only special messages as a way of having two groups of people but one of them will get all messages so its not really what you want.  

Two groups is the simple and best solution.  Members only need a single Yahoo profile to be a full member of all groups.

Answer 2

No, sorry, there aren't any options like this.  You would have to have 2 separate Yahoo groups, one for friends and one for family.