I'm trying to make a TL about the House of Hohenzollern getting elected into the PLC or inherit the throne of Poland, and I need some PODs to start where I would research. The POD has to be around the Jagelluons and the PLC.
Several times Hohenzollerns were close to Polish throne. the best PODs are:
-Władysław II Jagiełło has no sons, his daughter Jadwiga (Hedwig), bethroted to Frederick Hohenzollern succeeded him (no Polish-Lithuanian-Brandenburg union in such situation because Sigismund of Luxembourg would demand Frederick's father to name another successor for Brandenburg to avoid situation, when Polish king is also elector of HRE.
-Sigismund Hohenzollern (1538-1566), son of Hedwig Jagiellon and Joachim II of Brandenburg lives longer-if he outlives his uncle he'll be obvious candidate for throne of PLC in 1573.
-Albert Frederick (born 1551), son of Albert, Duke of Prussia, is sane and decide to convert to Catholicism and run for Polish Crown in 1573 (he was great-grandson of Casimir IV of Poland via his paternal grandmother, Sophia Jagiellon). In this situation he would have something later elective kings of PLC dreamed about-besides elective Polish Crown he'll have hereditary Ducal Prussia, thus his descendants have big chance to turn PLC into hereditary Hohenzollern realm over time.
Elector Frederick I wanted Polish throne for his son on one hand, on the other hand he tried to avoid open conflict with Sigismund of Luxembourg, and he had enough sons to split his inheritance-Poland, Lithuania and Brandenburg would be simply hard to manage for one man.
It seem to me if another Catholic dynasty become kings of Poland, it will have little macro historical effect. It will just be another dynasty which the Sejm will sabotage and which will pulled down into the fall of the Polish state.
It's easy to say that Poland is fated to political gridlock and decline. But that ignores the counterexamples of Russia, on the one hand, and Austria-Hungary, on the other. The fundamental problems facing Poland, like that of Germany was a failure of a royal dynasty (although the Habsburgs made a fair go of it, and even with the Reformation might well have succeeded with a fair bit of effort, say no Spanish inheritance or else the Burgundian Netherlands remaining with the Austrian branch) to consolidate central authority over successive generations. Geography also hindered Poland, less due to her size than due to the openness of her borders. A Hohenzollern Poland does several things: it gives a strong royal dynasty, which is able to gradually consolidate power in a manner similar to Habsburg governance in Bohemia and Hungary, it gives Poland a stronger western border (as it is inconceivable that this union would fail to make a play for Pomerania, and very unlikely that they would not gain it earlier than Prussia did OTL; and even without that, Brandenburg already brings with it part of the Oder border due to the Neumark), it gives the royal dynasty an Electorate- ensuring that they have constant leverage over the German Emperor, and in fact may well prevent the Habsburgs from maintaining their control over the crown- and prevents Brandenburg Prussia from emerging, it gives wealthy and relatively urbanized territory which, again, serves as a counterbalance to the Sejm's influence, and if they can peel off Silesia as well (eminently possible given the crises facing Bohemia-Austria-Hungary in this period) they would have a very defensible border with a very wealthy province. Add to this that a wealthier, more secure Poland, which has gained control of Prussia, Silesia, and Pomerania, would potentially be able to intervene in the east against Muscovite expansion, potentially forestalling Russia's formation if not derailing it entirely.
You can do what I did and have Hedwig marry Frederick II of Brandenburg, creating a Poland-Lithuania-Brandenburg union if her brothers aren't born.
As to the consequences, well obviously Prussia never exists. This Poland will probably scoop up Pomerania and Prussia earlier, and probably take Silesia at some point as well given Bohemia/Hungary's problems. With an electoral vote, and a strong independent powerbase, TTL's Polish Commonwealth is a major power, well positioned to dominate the Baltic and consolidate northeastern Germany.
Making the Hohenzollern Catholic will not give the Poles a strong dynasty, it will just make the Hohenzollern weak. The Vasa and Wettins was powerful dynasties, the Poles succeed in pulling both down with them. The Hohenzollern became powerful because they was Protestants.
For this to happen you still need to address the core of the problem, which is that the nature of the Sejm kept the Polish state decentralized and weak. A Polish equivalent of Louis XIV basically.
The Hohenzollerns became powerful because they had four successive capable rulers and a lot of luck, which allowed them to centralize and turn Brandenburg- described by Frederick the Great as sandier than anywhere but Libya- into a major power. If anything they succeeded in spite of their religion rather than because of it, due to the Great Elector's conversion to Calvinism over the Lutheranism of his subjects..
Hohenzollerns are going to turn into TTL analogue of Habsburgs. Catholicism did not prevented Habsburgs from turning Austria into powerhouse.