So what would happen historically I imagine the Mongols returning within a few years and crushing feuding Rus' princes and the Polovstians, or would they instead focus else where on Eurasia? This situation is kinda like the Battle of Tours except the IOTL losers have the resources and energy to return, but what if they lose in that battle too? Perhaps a Rus' prince alligns himself with the Polovstians and manages to build up enough defenses to defeat the mongols again? Is this feasible?
Well, it's nothing like Tours. As has been pointed out multiple times, Tours was a raid, simply a raid, albeit a large one, not an attempt at conquest. It was more a SIGN of the change in balance of power between Christendom and Islam than the CAUSE.
Here, you've done nothing to change the power dynamics, and nomad archers (if well organized) who can concentrate their forces wherever and whenever they wish have a distinct advantage over sedentary farming societies, whose military can't be as large (as a fraction of the population), and which is not as mobile.
Basically, until gunpowder allows untrained/semitrained peasants to be about half as useful as a trained archer, sedentary societies can't really leverage their greater numbers.
So. I don't see how the Russians can hold off the Mongols long term.