Families are complicated, even when the people involved aren't kings and dukes. Mix in a monarchy and you have a perfect recipe for some good old-fashioned family drama. In this play, several characters are trying to figure out how to act when cousins, sons, and fathers end up politically opposed. It doesn't help that the two guys fighting over the crown, Henry Bolingbroke and Richard, are cousins, both descended from Edward III, who everyone seems to think was a great king. Even though Richard is politically the legal heir to the throne (mostly because he inherited the crown from his father), Henry Bolingbroke seems to have more in common with his grandfather – and more of the qualities that make for a good ruler.
The play also asks us to think about whether family ties should be stronger or more important than political alliances. The women in the play choose family loyalty every time, while most of the men don't. Family is obviously a powerful category with major political consequences.
Since the crown could only be passed down from father to son, the fact that Richard doesn't have a son makes his hold on the throne that much weaker.
In Richard II, family cannot be separated from politics.