Some people just can't be reasoned with, some respect power, but most want peace for their kids. They want a future and they see men in suits in capitals far away from where they live making decisions they think they should be making.
You talk about Chechens, but there are pro Russian Chechens and anti Russian Chechens and Chechens that are happy to support either or don't care.
At the end of the day you need to embrace all the different cultures within your countries boundaries and have respect for them all, just as you respect religious choices people make.
To take the Middle East as an example Israel gives all the power to the nutter. When a bomber blows something up they end peace talks because they really don't want to make political concessions anyway.
They give all the power to the bombers and maintain a situation for the Palestinians that can't continue because the Palestinians have no future in the current setup.
The problem is radicals that are prepared to use force to get what they want. This includes Chechen radicals and Russian radicals and US radicals and Jewish radicals.
The only way forward is to engage moderates... don't blame all Chechens for the acts of a few because that alienates them and makes it more a case of them and us. Find Chechens who want peace... I always thought the Americans should have engaged Muslims more to get them to vocally oppose the violent actions of the radical few... it would clarify the real situation as being a few idiots rather than a war on Muslims.
The reality is that the US media has misused its power and will paint anyone who opposes the US in the Middle East as being an Arab terrorist. As if carpet bombing civilians in German cities during WWII from 20,000ft is not a terror weapon.
Look at how Arabs are portrayed in US movies, or Russians for that matter. There are exceptions of course, but Russians are drunk and steal US technology (modern Russian satellites apparently use programming code from US satellites from the 1970s it seems... according to "Space Cowboys" and are always full of nuclear weapons... Space cowboys and Goldeneye...).