Russia is not interested in split Ukraine. It does not need a fringe lawless state with conflicting ragtag bands, as it was in 1918. What Russia needs is an independent neutral (with possibly a slight bias towards Russia) stable Ukraine, which can act as a trading partner and a buffer zone with regard to cancerous NATO expansion.
Russia want the eastern provinces of Ukraine to join the Eurasian customs union (which includes Belarus and Kazakhstan in addition to Russia). I don't think that Kiev will agree to that demand.
Um, I haven't seen such demands from Russia. Where did you read it? I know that Russia would like to see Ukraine (as a whole) in the Customs Union, and that was one of the triggers for the whole circus, when Yanukovich did a 180* degree turn from EU to Customs Union, seeing more trading potential there.
On another note, a retelling a dialogue from the 12th of April meeting of the leader of Radical Party Ljashko with electorate in Lugansk:
Question (in Russian): - How much more can we tolerate this chaos in the country?
Ljashko answers (in Ukrainian): - Unless you speak Ukrainian to me, I will not be understanding you!
A woman's voice from the audience (in Russian): - Can someone already punch him?!
- Cкoлькo мoжнo тepпeть этoт бapдaк в cтpaнe?
Ляшкo:
- Якщo ви гoвopитe pociйcькoй мoвoю, я вac нe бyдy poзyмiти!
Жeнcкий гoлoc из зaдниx pядoв:
- Дa дaйтe жe eмy в мopдy!
Herein lies the problem to the Ukrainian split. Distilled.