I see you almost quit this discussion (and I am going to do the same :)) Just curious if you can read Russian, I am sorry, I could not find anywhere English translation of
this article, not on the Net, anyway. This is an old paper by G.V. Vernadsky published in Prague in 1925 where he analyzes two ways that Russia had to confront the Mongolian invasion. Prince Daniil of Galich has decided to side with the West and with Poland in particular as Christians against pagans and Muslims. As a reward, Galich was conquered by Polish King Casimir III. Galich is now called Galicia and our (other) Polish friends do not even think that this area has anything to do with Russia.
Another way is symbolized to Vernadsky by Prince Alexander Nevsky, who first fought both West and Mongols and later had to collaborate with Mongols in order to repel Western invasions (by Teuton knights, Poles and Lithuanians mainly). It was not a pretty decision and its consequences are still felt but it turned out to be better for Russia than to have anything to do with the West. Funny enough that approximately at the same time yet another ruler got his version of the Western help. I mean Byzantine emperor Alexius IV Angelus who invited Crusaders to help him to return to Byzantine throne. You probably remember what did they do instead.