To tell a personal anecdote about that option: back in the summer of 1994 (few months before the whole thing with sending troops to Chechnya blew up) I was going for a vacation to the Black Sea coast together with my family. On a train.
Train was robbed while on route through Krasnodar region countryside. It was robbed by a Chechen band riding horses Wild West style. It happened during the time when Russia was pretty happy to ignore whatever was happening in Chechnya and to allow Chechens to sort their issues among themselves. The problem was that Chechens weren't much keen on limiting their antics to their home republic. They were quite literally spreading the misery around.
I'll be honest with you. I am clearly younger than you are and to me all this is just history on a alternate history website. So while I do have sympathy for your ordeal and can value your insight when I look at stuff like this,
en.wikipedia.org
en.wikipedia.org
and I see at least a hundred thousand people murdered just as an estimate because Russia was determined to keep a region of people who didn't want them there and had very justified grievances to want independence.
en.wikipedia.org
Wars suck. Civil Wars suck. Every single kind of war is a crime against humanity because all wars are inhumane by their nature. The Chechen conflict directly contributed into the election of Vladimir Putin leading to the
*OMITTED DUE TO CURRENT EVENTS* and has overall be pretty terrible for Russia. So I would very much like to avoid Putin ever coming to power. Letting Chechnya and Russia amicably part ways might be a way to accomplish that.
I think you can agree with me Russia staying in the region did nothing to dampen ethnic hatred and that hatred would exist regardless if Russia stayed or not. My method at least means that the peoples of the Caucasus have to work through their problems themselves as their own Nation-States. Same thing happened in the Balkans, once the Turks stopped being a common enemy the region blew up. I know a lot of people died as a consequence of that. But the Balkans stabilized eventually after the Turks washed their hands of the region and the Turks are probably better off for it. Russia can play the role of mediator, it can send peacekeepers, it can keep a lot of soft power in the Caucuses. Would that solution be guaranteed work? Maybe not. In OTL Georgia fired its peacekeepers. Armenia and Azerbaijan alternate from being either at war or on the brink of war.
The point is that this Alternate History Challenge thread is trying to find what would create a best possible Russia, not stopping the Caucuses from blowing up, because that is impossible given the PoD and if we dwell on that bit too much, we are going off topic.