I don't think Russia has anything against the EU or Europe on principle.
Just to the extent that for some EU=NATO=Russophobia+general bias against Russia.
Obviously they object to that. I.e. what countries like Poland and the Baltic states do.

Finland for example has reasonably good relations and co-operation with Russia while also being an EU member, but not in NATO. For the most part Finland accepts Russia as it is. People in Finland are not scared of Russia because they know there is logic and consistency to how Russia reacts, it's not some rogue state that does random and crazy things. All sensible people in Finland (my neighbouring country) realise that NATO membership would be an extremely bad and counterproductive idea + it also goes against most people's ideological views too. Even though Finland was part of Imperial Russia for quite a while, Russia has no known designs on Finland.

Whatever you might think about Poland, at least they have chosen their path, stuck with it. As a result there is stability and an improvement in living conditions for large parts of society. Admittedly at a very high price. (mass emigration and brutal economic policies). But they are in a better situation than Ukraine, even though their economy was 1/3 of Ukraines in 1992, it's now twice as big.

The problem in Ukraine seems to be that they are so deeply split that while they are together, that they are just not making progress. The population is pulling the country in two directions, with the help of the superpowers and to the detriment of the population. While at the same time facing economic challenges. It's a formula for failure! The definition of madness is to keep doing the same thing and expect a different outcome. Ukraine has tried doing the same thing for almost 25 years now.I think the events in 2014 shows that status quo must change. Time to try something else, whether it's federalism, splitting up the country or a strong leader that makes them work together whether they want to or not. Just something different.

As for Belarus that you mention; they too picked their path and stuck with it. They have their challenges but at least everyone has a job, country has been modernied/renovated and is stable.
I don't perceive that as a Russian puppet; they took a different route to Russia and Russia is not running the show there. They just decided to orient themselves eastwards as opposed to westwards.

My impression was that Russia did not mind it if Ukraine managed to co-operate with both the EU and Russia. That's what RT says, anyway.
Whereas the EU took very strong offense at the idea of Ukraine working with both; and the USA even more so...

Maybe I got it wrong - but that was what I got out of putting both Russian and Western media options together and trying to discern the reality.

If ever there was a country stuck in limbo, it is Ukraine!