I have no real tips for dealing with sibling rivalry. My usual method of dealing with squabbling (petty or otherwise) is to–wholesale–send children to their rooms. I don’t want to play judge, I don’t care whose fault it is, and I don’t want to know who started it.
I feel the same way about CPS, CTU, and the state of Illinois right now. No one is acting like a clear-headed grown-up. Everyone’s blaming someone else. In both situations, I am the parent without a clue how to solve the squabbling, who can only wait it out, and hope that all my prior lessons and modeling of fairness will percolate through the surface while the child stews in his/her room.