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The two countries share much common heritage ...

That's like saying England and Ireland "share much common heritage." While true, the two sides tend to view that "common heritage" somewhat differently.

You could argue that the US has a right to control or have a sphere of influence over Great Britain because of our "common heritage." It's a weasel phrase hiding Russian aggression.

During the Kievan states period before the Mongols, the Kievan Rus moved north and brought Orthodoxy with them to the Slavic tribes north of what is now Ukraine. That's about the extent of the "common heritage." The rest is Russian imperialism.

After the Kievan states were destroyed by the Mongols, as the Mongols receded the Lithuanians moved into what is now western Ukraine. Lithuanian nobles converted to Orthodoxy to make themselves more acceptable to the Slavic population. When Lithuania formed a union with Poland, the Poles began to move in. They allied with the Zaporizhian Cossacks to move further east.

The smaller Polish landowners in the east and the Zaporizhian Cossacks started a civil war with the large Polish landowners in the west who were trying to muscle them out of the East. They were led by Bogdan Chmelnitsky, whose father was a minor Polish nobleman who participated in the occupation of the Moscow in 1608. The Zaporizhian Cossacks had their own grievances, chiefly the fact that the western Poles refused to accept them as szlachta: members of the noble class.

When the easterners were losing they made the mistake of asking Moscow for help and then, like others who made the same mistake, could not get rid of the Russians despite several revolts. If I recall correctly, by 1666 the Russians controlled what is now Ukraine east of the Dnipro plus Kiev. The rest they seized from Poland-Lithuania in the 18th century. That extra century of Polish control explains why western Ukraine is so different from the east, although Putin's alchemy has turned millions of Russian speakers into ardent Ukrainians.