I agree strongly with your assessment, its what I figured from what I've read. It also does not help that Jochi's legitimacy was called into question, because his mother was captured by enemies before his birth. And while the Empire may have splintered, it stayed together a lot longer than most nomadic empires.

I have a question, have you ever read the book "Genghis Khan and the Making of the Modern World"? It's an excellent book that I read. It doesn't focus much on the actual military tactics which to me is fine, since I already have a lot on it. But it is very good at adressing a lot of the misconceptions about the Mongols, and it discusses the reason why Batu withdrew (and comes to the same conclusion).