These situations MUST not be allowed to develop in the air.
According to
Le Canard Enchaîné, France's leading political gossip rag, the first Concorde flight from CDG to the USA (IAD) had just such a situation.
Tension started when the captain refused to carry the co-pilot's wife, none other than his own ex-wife. The co-pilot then bought a full-fare ticket for her and she got to board. It then seems the cockpit duo refused to address each other except through the flight engineer, who had to repeat everything barked at him by the one to the other.
This is with a planeful of folks like the AF chair, transport minister and other VIPs onboard.
Fortunately, there were no emergencies of any kind along the way.
People are people.