If Mary is wed to Sig before his first OTL marriage (my Anne Boleyn or Jane Seymour arrange it suggestion), then she's going to Poland.
Interesting. So Sigismund would in this case become King of England on Edward’s death, and Elizabeth would be cut out of the succession?
That Sigismund failed to sire an heir by three women suggests to me that he won’t have much more luck with Mary.
As a Queen of Poland, I imagine Mary becoming a big sponsor of the Jesuits and an enemy of the magnates, particularly those in Lithuania (especially the Calvinist members of the Radziwill family). Maybe she’d also be hostile to the Orthodox. But I don’t see Sigismund indulging all her anger—whatever Mary’s hostility to Protestantism, he’d be more likely to try and solve the English religious issue by trying to import the Polish-Lithuanian custom of toleration over the sea. Less ‘bloody Mary,’ more ‘Good King Sigismund.’
I stand by my earlier remark that it would probably be more convenient to split the domains in two—one son to ride herd on the Sejm, the other to keep the English from slaughtering one another. But that assumes Sigismund has heirs.
If not, then Elizabeth would still take the English throne (though I think her pragmatic enough to continue the Jagiellonian toleration). Might she stand for election as female King of Poland (“I’ve the heart and stomach of a king, and a King of Poland and Grand Duke of Lithuania at that!”)? Her religious convictions throw a wrench in that, but perhaps Warsaw is worth a Mass. If not, does Poland go the OTL Valois route?
For that matter, Henry III was one of Elizabeth’s suitors. He didn’t much care for Poland, or Anna Jagiellon, or Elizabeth (or women in general), but maybe his brother would push for the marriage more aggressively if it means getting three kingdoms under the Valois family.