You were suggesting that the parents find out what started it all, preferably by watching over the children and then deal with the culprit only to make things 'fair'. You were also suggesting that treating them equally and not taking sides was unfair and that forcing them into a position of having to co-operate to get back to doing better things than sitting in there room/s wasn't a solution as it would only result in more fighting.
If I've got that wrong perhaps you'd like to explain it again.