I think that the mindset that Islam wants to take over the world is simply media scaremongering.
The vast majority of Muslims are peace loving, as are the vast majority of Christians, but you get extremists who gain media attention and give the impression that their impact on the order of things is far higher than it is in reality.
Moslem extemists may continue to bomb, but that is because they are extremists, not because they believe it is a path to world domination. invasion of Muslim nations simply adds fuel to the argument that it is the West who wishes to rule the world, rather than the other way around - and on the basis or recent history, that argument does seem to have some weight.
By definition, it is not possible to rid the world of terrorism, but trying to assure other nations that we do not wish to force democracy on them might be a good start - and then backing that stance up by stopping the invasions of nations who do mebrace democracy as we do.
in the 60's and 70's it was the Communists who were set for world domination. Millions of lost lives later, did it move any closer to reality? No, and now it is forgotten - as are all history lessons, which is why we are doomed always to repeat them.