I believe they only want American troops out of the middle east and particularly Saudi Arabia IE the holy land and stop supporting Israel so the Palestinians can have their land back
They are quite happy to live in a diverse world if left alone
No, you are completely wrong on that one. The radical muslim believes it is his (or her) god (allah) commanded duty to eradicate the infidels (none muslims) and is commanded to do everything within their power (including suicide) to do so and to not do anything is blasphemy (for lack of a better word).
The reason the US is "over there" is to prevent any more attacks here. The US was drawn into the fight via a well staged plan by the radicals and Bush fell head first into their plan.
I mean, it was a long drawn out foreign policy by the US to get to this stage but none-the-less, this is where we are now.
The only way a "less hate" method of peace would work is to get ALL muslims on our side before the radicals get their mitts on them. But that will never happen as even if the radicals cause a mass evacuation, the US or allies will be blamed.
As much as I hate to say it, the ONLY way to eradicate the radical threat is to eradicate them, period.