There has always been a feeling of rancour between the two families.

Rancour : bitterness or resentfulness, especially when long standing.
Rivalry : competition for the same objective or for superiority in the same field.
Competition : the activity or condition of striving to gain or win something by defeating or establishing superiority over others.
Friendliness : the quality of being friendly; affability.
Suspicion : a feeling or thought that something is possible, likely, or true.

Antonym of Rancour is Friendliness