If I had more information, I might be able to say more about what, as a GM, I might do - for instance, what scenes would I frame, what antagonists would I put into play. More information would also help me understand what the players think they are doing. Does each player think his/her PC is being a genuine paladin, or not? To me that is very important for how I would deal with the situation as a GM.You might sincerely be confused, I cannot honestly deny you this, but you are the only poster which is demanding more details for what I believe was a decently drawn hypothetical. Perhaps he already denounced his father in public, perhaps he already tried to raise opposition - hence the reason for his banishment from the kingdom.
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I do not believe more details would change it (your answer), then why do you even bother making these kind of statements about the 11th hour...and so on?
Without that information, I can't say much more than I already did, namely that this is the sort of conflict between characters that actual play resolves. If I did know more, I could say more about what steps I might actually take to help frame and resolve that actual play.
I am sorry you feel that I haven't treated your hypothetical with the respect that it deserves. If it is any consolation, I have been posting for the past several pages about an actual play example in which I do have all the information ready to hand.