Dachspmg said:
Why did the Mongols bother with Russia and Vietnam, then? Europe in the thirteenth century wasn't particularly poor; the Sung may have been richer, and Khwarezm was probably much richer, and Baghdad probably still had some money left despite the decline of the Abbasids, but there was definitely wealth in the Italian cities, in Iberia, and in the Rhine Valley and the Low Countries (the former of which served as a power base for the Holy Roman Emperors in their incessant struggles with the northern Italian leagues and the Pope; the Hohenstaufens never could have done what they did for so long had all of Germany been an "economic backwater"). As for the inability to conquer Europe later on, I agree, because they couldn't have done it in the first place.
I think the Mongols may have viewed Europe as a potential ally. During the Mongol invasion of Eastern Europe, the Mongols made contact with the Venetians in the Crimea, who gave them information in exchange for the Mongols not pillaging their trade routes. Much later, the Ilkhanate sent an envoy (Rabban Bar Sauma, who had the distinction of being the first person to travel from China to Western Europe) to Europe to negotiate an alliance against the Golden Horde and the Mamluks.
The Mongols were actually quite serious about attacking Europe in the 1230s and 1240s, as their commander Subotai had heard that it was a rich land. When they beat Bela of Hungary, they sent assassins to hunt him down, like they did with the Shah of Khwarizm. But then Ogodei Khan died, and the invasion force had to withdraw to elect a new khan.
The other Mongol leaders weren't as enthusiastic of conquering Europe as Subotai, not because it was an "economic backwater" as such, but probably more because it was too far from home. Remember, Sung China and much of the Middle East is not yet conquered, so the Mongols might have thought it would be better to deal with threats (and treasures) closer to home first. An additional reason could be that the new Khan, Guyuk, doesn't trust Batu Khan ruling the Golden Horde in the west. He recalled Subutai from Europe and sent him to China. Batu Khan, meanwhile, had no interest in invading Europe as long as he was unsure that his eastern frontier (with Guyuk) will be safe.
By the time of Batu's deaths, the Mongol Empire was seriously fragmented. Kublai Khan only have nominal control over his "Il-Khans" in the west, who began fighting each other. As MilesGregarius said, with the Golden Horde and Il-Khanate busy trying to destroy each other, neither had the time nor resources to launch a serious attack against Europe, and Kublai was crippled by the various campaigns against his neighbours and also by the "tyranny of distance". By the time of his death, the now completely-fragmented Mongol Empire had effectively ceased to be a serious threat to Europe.
Had Subotai had more time back in 1241, when his forces are at the gates of Vienna, central Europe might've well fallen to the Mongols. Europe at the time was anything but united. The Mongols have already shown that it can easily annihilate apparantly well-armed, well-organised European armies, at Legnica and again at Mohi. The failure to conquer Europe after the 1240s was not because of military inferiority, nor because Europe was an "economic backwater" (although at the time China and the Muslim world were indeed much richer and technologically advanced), but because, as you said, the Mongols never got the chance. Their empire had grown too large, and fragmentation was inevitable. Even if Subotai had conquered Europe, Mongol Europe would've broken away from central control soon after. In the end, for all the glorious conquests, the Mongol Empire in the end proved unsustainable and it went the way of Alexander the Great's Macedonian Empire, to be carved up and fought over by competing lords, generals and governors.