at loggerheads

Engaged in a quarrel or dispute, as in The two families were always at loggerheads, making it difficult to celebrate holidays together. This term may have come from some earlier meaning of loggerhead, referring either to a blockhead or stupid person, or to a long-handled iron poker with a bulb-shaped end that was heated in the fire and used to melt pitch. If it was the latter, it may have been alluded to as a weapon. [Late 1600s] For a synonym, see at odds.

The adjective has one meaning:

Meaning #1: in a dispute or confrontation