While I agree that would probably work, my first instinct was to put the whole genocide option on the backburner. It might be a simpler option to just make their ideological position impossible for anyone with a child to rally behind. Right now they claim the west is evil and imperialistic, which people latch onto because, like you said, they were children when America invaded and bombed the shit out of their homeland. Helping the region's kids instead by supplying the tools for a better life would leave both them and their parents in the west's debt. It might take time, but eventually it would really take the wind out of these extremist groups sails. Why take arms up against someone you're indebted to and to an extent dependent on?
I guess it's just me being too optimistic.