Terrorism would not cease if Chechnya is left alone independent. Quite the opposite. In the period from 1996 till 1999 Chechnya was de-facto independent (check the history of the conflict). Instead of 'building a peaceful life' the power there was seized by organized and quite numerous bands. All civilization ended and Chechnya rolled back to a very brutal feudalism.
Moreover, terrorists' attacks did not cease, they intensified instead. Abductions for ransom became normal there. Chechen leaders lived by assasinations, abductions, drug and arms trade. They ruled their own people with animal-like brutality. At the end a whole army of well-equipped and trained mercenaries invaded the neighbouring Dagestan and there were three explosions of apartment blocks in Moscow and Volgodonsk. This is where the Federal Army intervened again. And the campaingn of 1999 was aimed not to merely 'pacifying' the Chechens, but extermination of all their leaders and all mercenaries. FSB made a thorough job and eliminated nearly all of them and at the same time it effectively blocked the Georgian border. Only after all foreign influence and all sources of funding had been blocked and criminals had been killed a resemblance of what we call 'normal life' returned there.
The terrorists themselves declared that their goal was establishing an islamist state in the whole southern region of Russia and adjacent countries to wage 'holy war' upon the heathens (i.e. us).