So, puppet government. I thought you wanted the dictators away, not support them. Because well, that's exactly what the West tried to do with supporting Kadaffi and co. Only this time with "rigged" elections*.
Not a puppet government, just one controlled by people who can work with the West. From the initial point the basic law can be set up by secularists, effectively shutting Islamists out indefinitely. After the first election we should leave them to stand on their own since the basic problem has been dealt with.
Turkey had a Secular government for fifty years. First election, AKP wins massive amounts of votes. Just staying for one election won't work.
Besides, Orthodox muslims can work with the West. See, the Libyan oil deals or well, Turkey. That's going fairly well for more than a decade (As opposed to Turkey's previous secular government, which was strongly isolationist). And Iran**'s doing fine in it's relations with Russia.(*) The West doesn't equal America, after all.
*And was in fact, one of the first to criticize the Taliban rule of Afghanistan. (See, you got different flavours of fundamentalism)
**On a side note, what has this one done wrong to deserve all the sanctions. Sure, they're developing nuclear weapons without permission, but so did India. And it's not like they're the most islamistic government in existence. That would be Saudi Arabia, which is an US ally.
Violence provokes violence. Yes, leave the groups alone. Focus on the actual problems, maybe attempt to talk with the more moderate factions. The Fundamentalist groups are only held together by the threat of a mutual enemy. Remove the enemy, and they will eventually collapse(or at least decline in popularity).
They are held together by their mutual belief in a vindictive all-powerful deity. They aren't going to just stop.
A Vindictive, all-powerful deity who doesn't do anything. Fundamentalists aren't dumb. They believe God send them to battle the great enemy. Without enemy, the organization will fall apart.
First, the problems here are of a different nature. They're not ideological. They're about pure dominance for its own sake. The powers that be in the U.S. don't victimize others over ideas, they do it for their own luxury. It's a pure predator/prey situation, and the only option when you're prey is to fight back.
Of course they're ideological! The intelligence agencies need to know everything about everyone so they can stop The Terrorists (TM), the corporations need to be allowed to do whatever they can to Create Jobs. It's all ideological.
Second, I don't expect existing fundamentalists to change, but not everyone in a religious culture that includes fundamentalists is going to be one of them. But when you attack a culture because of some fundamentalist element, it has an effect on the more moderate population as well. They see everything they know and care about hurt, and are naturally going to be less likely to want to understand their aggressors.
The fundamentalists can stay. They just need to stay in their mosques and out of the statehouse.
Not going to solve any problems that way. When the fundamentalists will find that the legal way to address their concern is blocked, they will try it in other ways.
As for examples of this happens. High ranking religious teachers in Iran of all places are proposing secularization. There were some steps going in that direction, but they're being lost in Iran's economical crisis. Sanctions are hard, after all.
I have no admiration for people with what you call a strong will, but I call bullheadedness. All those people do is fight with each other. They cannot be dissuaded, and catch everyone else, who would otherwise be capable of working out their problems in other ways, up in the middle of their violence. I cannot call it a good quality, when the world would be better off if no one had it.
Aren't you the one who was all "stand up and shout" during Occupy?
There's a difference between standing up for rights, and refusing to even listen what others say based on your own prejudice.
Also, a difference between peacefull shouting and military intervention and seizing control of another state.