Family is a very subjective word. People today tend to think of it as a group of at least one adult and one child who are biologically related and live together. But a young person in her twenties might consider her friends to be her family. Ancient cultures considered the entire tribe to be one big family and shared child-rearing responsibilities as well as other familial 'duties.' And then, what about an adopted child? Obviously blood relation, age, and size are variables. If we wanted to be Wittgensteinian about it, we might say that the word 'family' has a family of meanings (I couldn't help myself).
With so many possible iterations, a family is not inherently anything other than a group of people related in one way or another (biologically, relationally, etc.). There are families with two female parents, two male parents, single parents, no parents at all. Furthermore, gender roles are promoted consciously or unconsciously by society and by individuals; but they are not inherent in any social structure per se.
An anarchistic family would be similar to what Max Stirner called a "union of egoists"; it would be a group of individuals who act according to their own wants and desires and commiserate and assist one another because they want to do so. I think a family like this would be steeped in authoritative values whereas a hierarchically structured family would be based upon authoritarian values.
The difference between the two is that an authoritative family would have certain agreed upon rules or morés that everyone voluntarily accepts; all understand the reasons for the rules and respect each others' autonomy. And, if a member no longer wishes to follow the rules, they can leave the unit, petition to have them changed, or just ignore them and see what happens. Speaking of a parent/child family in this way might sound like a utopian pipedream, but I think children respect explanation much more than threats (who doesn't?). Every child will test boundaries and hell raise (and that's good). The important thing is that their parents reveal to them--by example and through explanation--the logic behind their positions, but also that they give their children breathing room to create themselves at the same time. This breeds responsibility and independence. Parenting--like teaching--should NOT be an assembly line job, cranking out carbon copy children/citizens. It's that kind of thinking that leads to the construction of an authoritarian household, one run by self-proclaimed alphas who rule with iron fists and drag out the old standby "Because I said so," coercing other members into submission by advertising their superior might.
Still (and I hope I'm not alone in this) I think that force is sometimes necessary in familial relationships. If my child is running toward a busy intersection and will not heed my warnings to stop, I would be a fool to let him go. A good parent scoops the kid up and THEN explains the logic behind his action. Or, if a close friend of mine climbs behind the wheel of his car after downing five whiskeys, I will take his keys by force if he is too belligerent to offer them up.
Let's not forget: Humans are social animals; we crave love and companionship. The family is a fluid, complex institution that can be bad or good depending on its members, but it will never disappear. Besides, the typical nuclear family has never really been typical anyway...and that's good. People should be encouraged to freely associate with whomever they wish and to form or join families that suit and fulfill their own unique personalities. Therefore, regarding your last point: to abandon the family altogether (if we are using my broad definition) would not only be impossible and pointless, it would also be downright detrimental.