Kiev Rus, I think, got swept by Mongols like everyone else up to Hungary. Moscow somehow emerged as a new player later on under Mongols – some say that Moscow centralization and cruelty are coming from their Mongol origins, this is not a fact, but an opinion that might come from their enemies as you are saying. But the fact that area of Moscow (probably a village at the time) was a remote part of Kievan state does not make Russians the owner of that. If you wish, this is like Canadian appointing a new King because they used to be part of the Empire… In fact, if you insist that there is a kesher, then Ukraine should be in charge of Moscow.
The analogy with Palestinians makes a lot of sense though. As my Israeli friend quipped about some peace negotiations: why do I want to be a cousin of people who kill their own brothers. Same, if Russians are claiming that Ukrainians are their brothers, then why do they send Chechens to kill 10,000s of the brothers, and now destroy power for millions. This is not the way we generally understand “achicha”.