We don't normally think of government as anything beyond civil government, but there are in fact four spheres of government, including self government, church government, and family government, and civil government is just one of these areas. It may not be obvious that family is a legitimate form of government, but if we ask ourselves the five questions of government, it becomes more apparent.
The first of these five questions is a question of sovereignty. Who's in charge of any family? The parents, of course. The father is often seen as the head of the family (but many husbands admit to their wives actually being in charge), but it is obviously a 'team effort'.
The next question is of hierarchy. Who reports to whom? The parents are in charge, and have ultimate jurisdiction over their children. Of course, in a 'clan' setting, there would be a hierarchy with multiple levels, but in a single family the parents have ultimate authority.
The next question is one of law. What are the rules in a family? Obviously, rules differ from family to family, as parents set their own rules according to how they wish to raise their children.
Next is a question of sanctions. What are the rewards and punishments for obeying or disobeying? Parents may choose to reward their children with privileges such as 'dessert' or 'TV', and punish their children with spankings or removal of privileges.
We next have a question of succession. Of course, a family's children will grow up and have their own families, thereby extending the line of their parents and expanding the family government.
We can conclude that family is an institution of government, as well as self-government, civil government, and church government.