Personal union between Polish-Lithuanian Commonwealth wasn't easy to maintain. No surprise it ended with disaster. Catholic King of Sweden residing on the wrong side of Baltic, with treacherous, power hungry uncle as regent, had very little chance to keep both crowns. So what if such union never happened? There are many ways to prevent such union.
Say, that John III of Sweden has one more son (his short living oldest daughter (born 1564) with Catherine Jagiellon is born as healthly boy instead, named Sigismund. He is followed by John jr. and Anna. TTL Sigismund is a bit similar to OTL Anna Vasa-disapointed with Catholic Church he converts to Lutheranism, but still keeps good relations with his Catholic brother (John jr is analogue of OTL Sigismund Vasa). So King John had big problem he faced IOTL solved-he could provide both Sweden and PLC with heir of right religion. John Jr Vasa would be the one winning election in PLC while his Protestant older brother would succeede father on Swedish throne. With Lutheran monarch residing in Stockholm Charles of Södermanland had little chance to take the throne, so he'll be either loyal or dead. What else changes? Among others:
-PLC and Sweden would have peaceful realations at least as long as brothers are still alive (until 1630s)
-Jan II Waza, King of Poland, not having to deal with uncle Charles, could concentrate on his another opponent-Chancellor Jan Zamoyski (who IOTL hoped to turn Sigismund III into his puppet, and seeing, that young Vasa is not willing to be his pawn, Zamoyski became fierce opponent of the King).
-Likely there would not be Swedish involvement in 30 Years War (which may not last 30 years ITTL) and no French subsidies for Sweden. ITTL Sweden would rather not be such warlike kingdom like IOTL. And Denmark would be regarded as stronger of Scandinavian monarchies for much longer time.
-Ducal Prussia is likely incorporated by PLC after death of Albert Frederick in 1618 (not only nobility of PLC but even Prussian estates wanted it, knowing that Elector of Brandenburg would not respect their rights. But Sigismund needed Protestant ally against his Swedish cousins, thus he agreed to pass Ducal Prussia to Electoral branch of Hohenzollerns.
-PLC and Sweden would cooperate against Russia during Time of (even deeper) Troubles.
-Wars about Livonia (which were continuation of war over Swedish throne between Sigismund and Charles) are avoided, PLC keeps Riga.