Now this is quite an original PoD.
A couple thoughts:
1) This union sticking together wouldn't be any more unlikely than the Hapsburg realms of OTL. The eastern Hapsburgs held dominion over Flanders, Wallonia, bits of Italy, Austria, Bohemia, Silesia, Slovakia, Transylvania, Hungary, Croatia, Bosnia, Dalmatia, Southern Poland and Western Ukraine. Most of those at the same time. The Eastern Hapsburg realms more geographically and culturally diverse than these alt-Jagiellon kingdoms. Not to say that this personal union would be easy to keep together, but it is possible.
2) Most European kingdoms had problems with nobles trying to erode royal authority, and most of them had times when the nobles were on the ascendant. My reading of Polish history is that the crown was not so much inconvenienced by the golden liberty, it was more that the crown lacked it's own secure power base, and thus had to honour the laws limiting their power more carefully than the king of France or of England, say.
The Hungarian Jagiellons would have more legitimacy than the post Jagiellon kings of Poland and they would have more power bases with which to draw strength to oppose the magnates than, say, the electors of Saxony could.
3) No Polish Vasa dynasty would be a great thing for Poland. The attempt to unify the crowns of Poland and Sweden by the Polish Vasas brought only trouble.
4) I would be interested what the relationship between Jagiellon central europe and Muscovy would be like... And what the Muscovy-Ottoman relationship would be like. My bet is that Russian-Ottoman relations will be better in this timeline, since both will consider the Jagiellons to be the greater threat.
Certainly I'd love to see a TL about how this works out. Even if the union of crowns falls apart, it's going to change Europe in interesting ways.
fasquardon