I know the EU doesn't have a history of coordinated military action. But if tanks crossed EU borders France, Germany, Britain and Italy couldn't ignore that.
You can't really judge how an alliance will respond to conflict crossing their borders on the basis of how they've responded to conflict outside their borders. Governments and militaries think borders are a pretty big deal!
More generally, there are some people in "the European project" who would like to see a United States of Europe with its own foreign policy and military. But this is pretty unpopular with voters in most member states, so everyone involved is happy to keep that level of integration on the back burner, leaving member states to respond how they like to foreign military conflicts while the EU maintains "We're a pacifist trading union, not a belligerent military alliance or a superstate, shucks we don't even have a military"
Politicians are happy to keep kicking the can down the road on EU military coordination for as long as it's politically convenient. But if an EU member state was invaded, they couldn't do that any more; they would have no chance but to make a decision.
And public opinion is far more likely to support (and may even demand) a tough, belligerent stance if Russian tanks have are invading our allies.
Crimea was part of Russia longer than the US has existed. While its previous host, Ukraine, has only existed as a country for 20-some odd years.
Once the government of Ukraine was overthrown, the people of Crimea had every right to decide to stay or leave. And you will not find a single poll before-or-after not showing an overwhelming support for the latter.
> it was Ukraine snuggling up to the EU that provoked Russia into intervening...
A foreign-lead coup of a twice elected democratic government that put in a puppet regime for the sole purpose of creating problems for Russia is what lead things to the way they went.
Right now, what is happening in the eastern parts of Ukraine is a civil war - resulting from ethnic cleansing, neocon agenda, etc. And what is happening in the west of Ukraine is a total economic collapse from the so called free-trade deals with the EU.