Like many others: It depends.
I like JoeGKushner's answer best.
Personally, I prefer to avoid the problem at the start. Strictly IME:
You can play your Paladin as the paragon example of all that is lawful and good. You are here to set an *EXAMPLE* of the epitome of spiritual achievement. You show by how you live your life and perform heroic deeds what others can achieve... by following your example. You should serve as an inspiration for the lying thief, the uncouth barbarian, the greedy wizard, or the amoral mercenary to become better than what they are. Your god's view, and your personal view, is that it is better to gain a convert than a corpse. Requires the metagame condition that the other PCs cooperate with certain Paladin restrictions (such as "don't kill the BBEG after he surrenders"), and the DM not shaft the players with every bad guy who surrenders trying to murder them in their sleep.
Or, you can play your paladin as a crusader, out to squash anything else remotely resembling evil, and put to the sword anything that violates your code or the Lawful Good alignment. The "Convert or Die," approach falls in this category. Requires the metagame condition that the other PCs have their characters toe the line of the paladin's code also or be okay with conflict (even combat) between PCs. The DM must be prepared for this conflict, because it will probably happen suddenly and can wreck a plot or campaign in the time it takes to roll a d20.
Both types can be fun. The more like the second type the Paladin is, however, the more opportunities for trouble. It really depends on your group's play style.
If I'm running a campaign, the players are required to create characters who can work together. So my campaigns tend towards the first type of paladin. Either type is Ok in a one-shot I'm running (so long as the players know what they're getting into).
As for which one I'd remove: The PC (paladin or non-paladin) who continuously crosses the line between being DM-friendly and DM-unfriendly gets a talking-to, and can lead to retirement of the character or removal from the game. If I'm a player, whichever of the involved PCs is being the biggest pain in the posterior gets my vote for the boot.