Open up a can of U.S. whoop ass like we used to do.
Nope. Not gonna happen.
That would hurt their feeeeeeelings.
That's the first step ... the powers that be need to grow a pair and fight a war like war needs to be fought.
Step two is to decided if we want Iraq whole or in three seperate states. If the first option, we need to install a pro U.S. strongman and forget all the pie in the sky ideals and stuff and deal with the reality of the situation. Much like the old Yugoslavia and Iraq, when you've got a state with ethic issues, you need a strongman like Saddam or Tito to run the place with an iron fist. Find one and let him do his thing ... it won't be pretty, but it'll get the job done. If the second, we need to "manage" the disentrigration so Iraq doens't spiral into 10 or so years of ethic wars like Yugoslavia did.
Otherwise, we still need to try the Iraq armed forces and police units regardless, they need to be able to carry on the fight, regardless of which option. If the later, we end up training three seperate entities (Kurd, Shia, Sunni) instead of one.
Carve Kurdistan out of Iraq and Iran, and ally it with Turkey..take over the Sunni triangle and give it to the turkmen, Assyrians, and Chaldeans...let the Shia know what happens to our enemies, and assure them that if they don't play nice we know where they live.