I think this will largely fix itself over time. The reason is that the U.S. no longer needs the Middle East for oil. The price of oil has gone and stayed high enough that extraction from oil shale is now economical, and most of the majors are going that route. Which country has the largest oil shale reserves? The U.S, with total oil reserves roughly 3x greater than Saudi Arabia. We simply don't need the Middle East any more - I think that over the next couple years you'll see a complete U.S. pull-out from the region, and we'll leave them to their traditional customs and autocratic rulers.
Source: my sister's a petroleum geologist. When she was training in the mid-00s, all the attention was on light, sweet crude from Venezuela or Saudi Arabia. Now, virtually everything she does is fracking in Colorado or Wyoming, or work with the Athabasca tar sands.
Certainly the West should repair their relationship with others that have been affected by imperialist policies.
But that's not a panacea either. Islamist goals of introducing Sharia are incompatible with Western-style democracy so it may be possible to 'get along' but it won't be as simple as making nice on our side. Of course, we'll only 'get along' right up until the next citizen of a Western democracy draws an image of the Prophet Muhammad....
Likewise there remain nations with aggressive dreams of going above-and-beyond UN convention regarding resource rights, which is obviously incompatible with Western ideals.
There remain nations trapped under totalitarian governments strongly opposed to the West. However weak they might be we can't drop our guard completely.
So while I agree that the West has some apologies and amends to make I don't agree that would completely solve world peace, and I don't agree that all violence expressed against the West is "our fault".