One turning point might be the invasion of Hungary and the death of Ogedei Khan. After Batu and company had gone to all the trouble of destroying what was essentially the only army east of the Pyrenees capable of standing against them, the Mongols had overrun Hungary were all set for moving into Austria and beyond. Unfortunately for the Mongols, Ogedei Khan chose that moment to kick the bucket, most like as a result of his heavy alcoholism. As a result the Mongol generals had to return to Karakorum to elect a new Khan. This, combined with the various politicking that followed the change in leadership significantly delayed the Mongol plans for further expansion into Europe. Batu wanted to continue the Mongol invasion of Europe, but by the time he felt secure enough to try it again 14 years later he died before it got going.
Have Ogedei kick his alcohol problem and he would have probably lived quite a bit longer, allowing the Mongols to penetrate even further into Europe.
A similar thing was done in
Empty America, with Ogedei vomiting up poison meant to kill him after downing a bottle of Rum that had been given to him in tribute from a Frankish merchant. The ensuing Mongolwank is both brutal and terrifying.