I'm not airlines, per se, but operating a regional airliner to some sort of reasonable airline standard (one hopes).
We try to avoid this 'two captains' situation, yes, but given two mature adults it does seem survivable.
Whoever is named first on the roster is in overall charge and gets to nominate PF and PNF. That seems to keep questions about who is in charge under control.
We have done quite a bit of 'two captain' flying in the sim, when one can often see oddities develop in emergencies as the other captain tries to assert his (nonexistent) authority. This is when good CRM comes to the fore, hopefully. We have often come away from a session having learned more about CRM than the aircraft systems.
I think that the stronger the personality and the better the systems knowledge then the less problems about authority enter into the mix. The weaker captains seem to have more trouble staying on the uphill side of the authority gradient.
Check the epaulettes: the guy with the shinier gold bars is usually the weaker one. Well, that's been my experience.