Henry the Pious, Polish (Silesian) duke during the period of feudal disintegration of Poland was very close to reunifying Poland and getting Polish crown. However, his struggle was brutally ended by a Mongol invasion and his death in the battle of Legnica (Liegnitz). But what if Henry the Pious was actually victorious? It wasn't impossible (this scenario doesn't belong in ASB territory, Battle of Ain Jalut proven that defeating Mongols, was possible - hard to do, but possible - Mongols never bothered Mamluks anymore after the battle), so let the fun begin! Battle itself had quite a dramatic story, so let's introduce two crucial points necessary for Poles to actually win the battle:
a) First off all, in numbers Mongol and Polish forces were almost equal - Mongols had 8 thousand warriors, while Polish forces consisted 7-8 thousand warriors. The gamechanger was betrayal of Opolian prince Mieszko II the Fat, who escaped from a battlefield with his Opolian forces. Say Mieszko the Fat chokes on his meal just before the battle, leaving Henry II as a commander of his forces.
b) Silesians were waiting for a help of a king of Bohemia, Wenceslas I, but they never managed to join forces with Czechs. Say Mongol operation is less succesful than IOTL, and Poles are actually able to join forces with Czechs, so Mongols are actually outnumbered. As a result, battle is a Polish-Czech victory, when Mongols are forced to leave Poland. They are sure plotting the revenge, but Ugedey dies at 11th December 1241, so they aren't able to enact their plan. This leaves Henry (now regarded as a savior of Christianity and a defender of Mongol hordes) as a strongest duke in Poland. Death of Mieszko II the Fat strenghtens his position even more, because he is again a regent for his underaged brother, Vladislaus. Henry regarded as a savior of Christianity, has no trouble defeating Conrad of Mazovia (who is a mindless brute not liked by a nobility), and in addition Conrad's son, Casimir of Cuyavia (married to a Silesian princess) betrays his father and sides with Henry. Young Bolesław (son of Leszek the White) is raised by Henry and gives up his duchy out of piety and joins clergy (he is planning to become member of TO). As a result, Henry the Pious is a undisputed ruler of a majority of Bolesław's III legacy in TTL 1250. With a help of his Czech brother-in-law, Wenceslas I, Henry is crowned the King of Poland. How large is the impact of a earlier reunited, stronger Poland in Middle Ages? Teutonic Order gets more help against Balts from a strong King and it means that TO could do better in it's campaign against Lithuania. What's more Czechs are gaining an important ally against Hungary in struggle of Austrian (Babenberg) inheritance. Brandenburg cannot even dream about getting Lubusz land (Neumarkt) and Silesian presence in Lusatia continues.
@Jan Olbracht