It is in no country's interest to have a major war - that's true of Russia over a Ukraine in NATO and the US or Poland over a Russian dominated Ukraine. Would Russia do so nonetheless? I don't know. Would the Poles and the US, I very much doubt they would do so directly, but they would certainly adopt a radically harsher policy towards Russia which could easily lead to a spiral of escalation.

As for EU interests. Ummh, last I checked Poland and the Baltics were part of the EU, something you seem to be forgetting. If you mean the Western EU countries - that depends. To the extent that they adopt the kind of policy you and others here are suggesting, they can forget about any sort of EU-Russia cooperation that requires unanimity, they can also forget about any sort of treaties strengthening the EU. They also have to depend on the US deciding it will not agree to take up Poland and the Baltics on their request for closer military cooperation and US bases, and a more hostile policy towards Russia. Or to put it differently, if the US is as recklessly imperialist as you think it is, then your policy has a very good chance of leading to a European war. Also keep in mind that Russian can't supply the rest of Europe with energy if it doesn't supply Poland, unless the Europeans agree to compensate Poland for that situation with energy supplies at a similar price - all those pipelines, existing or proposed, run through or right next to Poland.

As for your politics 101 - the more accurate version would be, if you're in a region claimed by one power as its sphere of interest, and without another great power able and willing to back you up enough so you can make it too painful to ever attack, then you're better advised to do as you say. Think Cuba, Nicaragua, Chile, Lebanon, Syria, Vietnam, Korea, Hungary, Czechoslovakia, etc. Georgia made the wrong calculation.

The Ukrainian population isn't interested in joining NATO - if it were, then the risks for Russia would be far higher. Ukraine is a far bigger and more powerful country in it's own right, and it is much easier to help geographically. Russia would face a problem that makes the American task in Iraq look like a, ummh cakewalk (pardon the expression). But again, the Ukrainians aren't into the idea of paying a major price to be firmly in the US camp, so the issue is moot.

The Belarussians are being tolerated by the Poles, Balts, and Americans.