What is the best way to mediate a conflict between stubborn siblings?

If this isn't an ongoing conflict between them I would stay back and let them figure it out themselves, if you put yourself in the middle and they just get angrier about the conflict you will be pulled into it, and when they get over it, they still might be mad at you for interfering. If its an ongoing conflict it will never be solved, they're enjoying the conflict too much to resolve it. Family's fight alot but when it gets down to the nitty-gritty they will be there for each other.

Its hard but sometimes there isn't much you can do. Letting them find their own often times is much harder than being the go between. As long as they both are going to be stubborn and not listen, you will just have to wait it out til one of them mellows just slightly. Give'em some time. They will be okay.

invite 5 near and dear people fromeach side including their fat her in law and what ever decision taken by majority would be final, and should be acceptable. You have to make very clear that decision taken by the arbitrators have to be honoured by both(Kamath solved anil and mukesh dispute)