The eastern part of Ukraine is closer to russia in history and mentality, with many people being children of Russian & Ukrainian parents or have relatives in Russia. USSR didn't happen all that long ago either. As for mentality - they are often religious, orthodox christians and for them that liberal policy when it comes to relations of same sex etc. is a strong argument against europe. The worst insult here is actually the "gay" and insults always reflect what is "worst" in opinion of the people. Getting them to accept gays is the same as trying to get Muslims to drink, smoke and eat pork.
While it' not #1 in significance, it sure doesn't help many people to accept EU and is easily used by anti-EU forces for propaganda.
On the other hand there's western Ukraine which is very Nationalistic and have no love for anything USSR or Russia related, viewing it as invaders. On top of that the leaders of URA (if my translation is correct for "Ukrainian Rebel Army") have been known to be associated with Nazi back in WWII times (although they canceled the agreements later). Although URA fought both - USSR and Nazi, it is still strongly associated with these things by eastern people: "nationalism", "Nazi" and "anti-Russian".
And between East and West - there's "central" Ukrainians like myself, which speak both languages and kind of children of 2 cultures, these are usually less aggressive and don't care as much for "ideology" or nations but pursue economical prosperity for everyone and view corrupt government as worst enemy.
The key problem of it all is that when there's a problem and people are angry - politicians and radicals try to quickly shift their attention to this old "wests vs east" thing.
There's some truth in that because eastern people are known to care less for Ukraine as independent country and do not respect it's history, traditions, languag etc. and think of it as part of Russia. And the fact that most of the ruling party and president are from East doesn't help it either.
But what happens lately is that people from both sides are so fed with corrupt politicians they no longer care for any ideology. But fighting regime is one thing, building better one is another. I know for sure that opposition is no better, they just represent different kind of business interests - import oriented and unlike some Eastern guys they don't have any manufacturing/business here, they'll just sink us in imported goods destroying our own manufacturing. It's what Yulya did when she was prime minister.
Personally - I don't see any quick solution here. The core of the problem is in people majority of which are dumb. Noone protest for better tax system, business environment or laws. Most just want their salaries and pensions, not knowing i's our taxes that keep them fed.
One thing I'd start with - elimination of government business sector. No manufacturing, commerce, business should belong to government. Otherwise it only upholds the corruption, and we have too many structures that are 50/50 government/commercial and owners are none but deputies of high council themselves.