America's Antagonistic Allies

[headsplice]

Terrorism is all about the emotional reaction, so we're playing their game.

Bingo, you hit the nail right on the head. Ultimately, terrorism is a childish act. More concretely, terrorism is the act of someone who doesn't like something (say, the occupation of holy land by infidels) and then lashes out blindly against whoever has 'wronged' them. Al-Qaeda is, in one sense, the twelve-year-old on the schoolyard who sees a bully hanging out in their playground, throwing their weight around and striking back (the WTC attack is a proverbial kick to the nuts).
My question still hasn't been answered: how do we react to being kicked in the nuts? In terms of the playground analogy; we have to change from the playground bully (who has now not only kicked the other kid's ass, but now is sitting on him and giving him a wedgie, making him angrier), but we need to become some sort of (yes, I know, vague) principal or court appointed therapist figure that removes the offending child and the bully and makes them work out their differences.
I realize that the analogy breaks down somewhat (as analogies are wont to do), but, no one can say that our current tactics and strategies are effective.
So, someone come up with a better idea which does NOT include "nuking the shit out them" as that would only provoke another emotional reaction from them, pushing them closer to another act of terrorism, continuing the cycle.