What is incumbent upon one who missed the Friday prayer due to the long distance, and prayed Dhuhr in its stead?

What you did by going to visit your relative after the time for Jumu'ah (Friday prayer) began is a great sin for which you must repent. The jurists have stipulated the unlawfulness of traveling after zawal (the sun's declination past the meridian) on Friday for one upon whom Jumu'ah is obligatory, because its obligation is tied to the entry of its time. Allah has commanded hastening to Jumu'ah and forbidden being preoccupied from prayer after the second adhan (definition). Your performance of Dhuhr prayer is valid, but you must repent and regret your action.