Have you ever tried (once you sent each one to their room) to go into their room, and question each, not as to who started the fight but why all their disputes even happen. See what they dislike about eachother. If it's the case that they're too different, then you handle the matter by teaching them to accept any traits - even the ones they don't agree with and perhaps if the hatred between them isn't too big yet, try having a group session with them - approach the matter from a psychological perspective, perhaps the best case would be to actually have an educated counselor to guide all of you and truly "work things out".

If it's not their differences, but some foolish thing, or perhaps their bad past experiences. Then again you need to work things out from a psychological perspective.

You can say that you don't need counseling or help from a psychologist/therapist but here is a sad story I have for you:

"My grandfathers sons (my uncles) always hated eachother and still hate eachother till this day (even though they're around 40! - no longer little children). I'm not talking about any minor hatred like - I'll avoid speaking to you, or I'll ignore your presence, or I'll leave the room if you're in it - I'm talking about a genuine I will physically abuse you if I ever see you again. The one thing my grandfather longed for was to see his sons shake hands before he dies. Well ... he's dead now. Both sons did attend the burial and they even stayed in the same small room (for the wake) but this was a cold acceptance of eachothers presence. They will never shake hands because their hatred stems too deep - it started in childhood and it lasted till this very day, 40 or so years of dispute cannot be so easily mended, if at all."

So hear me on this - You do not want to find yourself in my grandfathers shoes - act quickly and act while there is still time. Above all act rationally and ask people educated on the field for help!