Honestly, I am less concerned with players fighting each other, since there are Red Alert pvp rules, which may be adapted to this kind of situation.
But consider Starfleet away team landing on one of Maquis’ worlds with orders to find and arrest one of famous terrorist. PC conduct investigation and find where is hiding place for Maquis group and now there are planning the ambush.
During this process one PC realizes that she has a family members involved in terrorist group. She secretly contacts them and information she gets change somehow view on whole situation. She considers that Maquis are not really bad and their ‘terrorist’ activity may by easily explained as a self-defense against some aggresive moves from Cardassians.
Now we have two agendas in our team: part of them want to follow Starfleet orders and really do not care about nuances of political situation and another part of team want to suspend the operation and investigate more, maybe even try to change orders.
Having this kind of conflict may be settled over a table between players and of course there should be a lot of debate and discussions, it can be ruled as a roleplay, where we all hear arguments from both sides and decide what to do next.
But from my experience I should be prepared that players want to settle this mechanically - similarly to fight, as an opposed check. Some of PC have diplomatic or persuasive talents (using momentum or threat), they may want to use determination even. Of course result of this task will be followed by roleplay, but I would like to know if there is mechanical support for this kind of challenges.