Russian war planning calls for winning a nuclear war with battlefield level weapons, they've been practicing it for many years. It's very reasonable to believe Putin (I started to type Trump) is deluded enough to believe that he can fire off a few small nukes . So, that makes it a much harder calculation.
What if he uses it strictly on a military target, say an air base in Ukraine? That's one scenario that could happen whether we go in or not. If so, how do we respond? Massive, overwhelming, conventional attacks while loudly proclaiming that we won't use nukes might work without it escalating. What if he decides to take out a city? We would have to respond in some way, probably the same way. However, what if he uses a dozen? That means he's gone over the edge, and the military either can't control him, or has gone all-in (as in the US, he can't by himself, launch nuclear weapons, there is a chain of command and checkpoints in the process). That's when things turn south, in a hurry.
To me, this will require a great deal of self-restraint on NATO, avoiding nukes while using our far superior militaries to take his out, while avoiding civilian casualties. Beyond that, we respond basicilly one for one, and hope one gets him, or the more sane General's do.
Personally, I advocate sending in a fleet of transports, Berlin lift-style (maybe 8 or 10) with humanitarian aid, escorted by very visible F-16s and F-15s, with a very quiet group of 4 or 5 F-22s flying high above. Declare a 30 or 50 mile no-fly radius. Be very visible and very transparent about it, especially the humanitarian aid part of it, with reporters on the planes, perhaps. Make it clear that any attacks on the air fleet will result in the immediate destruction of the attacking force, as well as a declaration of war by Russia. This puts that ball in Putin's court, and pushes every button he has, but in a way that the world will recognize who starts what. He probably backs off, and that's that. After that, we increase the aid flights and fill the sky with numerous aid flights, while ignoring his bluster. This makes his air operations very much more difficult.
The Russian game plan seems to have their armies retreating from a NATO "aggressor" and using the weapon on their own soil to minimize the political and military blowback, while dividing the West. If they start the next phase by attacking a humanitarian airlift, and we respond in kind, he doesn't have an option to nuke an advancing army. Then, does he fire on one of more NATO airbases.
Either way, especially if he only hits a few military targets, we hold our fire on the nukes, and go after them with every conventional thing we have. Also, since we seem to have hacked their comm systems, doing everything possible to delete said order and/or shut down his nukes, including GPS and other space assets, would seem to be in order.
Otherwise, I think we stay out, and let Russia sort this out. Frankly, I believe it will, and sooner rather than later. Putin's days are numbered.
Fascinating, if scary, article from 2015: https://www.vox.com/2015/6/29/8845913/russia-war
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in the darkness
