When it comes down to it, family relationships, especially those between fathers and children, are at the center of the play. (Characters who are mothers, as several critics have pointed out, are noticeably absent in King Lear but there's plenty of talk about moms in this play.) Lear is not only a king, he's also a family patriarch whose plans to divvy up his kingdom among his daughters backfires, causing a civil war that gets played out as a large scale family crisis. Lear's family isn't the only dysfunctional crew in the play – the drama between Gloucester and his sons heightens the sense that King Lear is a decidedly domestic tragedy.
In King Lear, the aging monarch's crisis of kingship is played out as a distinctly family matter – in the play, civil warfare is literally a family squabble and Lear's most disloyal subjects are his unruly daughters.
Edmund's wicked actions are not those of a motiveless man – he sets out to destroy his father and half-brother because he objects to society's treatment of illegitimate and second-born sons.