If England stayed Catholic (many PODs possible, just take your pick)
Could Maria Beatrice of Savoy end up as Queen of England and Duchess of Savoy (OTL Savoy didn't allow duchesses, but let's imagine that bug gets out of the picture)?
And would it be possible for a England-Savoy-Austria Personal Union in the net generation with England still believing in the Divine right of Kings? Or I suppose maybe England-Ireland-Savoy-Austria...
The most recent POD closest to Maria Beatrice's birth would be the '45 succeeding. A whole generation (or two) came and went between then and her birth, so even assuming that there
would be a Maria Beatrice who's the same as OTL (and not born Victor Amadeus or dies in infancy) it's a long shot.
And as to this extremely stretched possibility that she becomes queen, there's a reason that some Jacobites don't consider her line of descent (not all, but certainly some). She married her uncle. Whether the pope okayed or not is irrelevant, since if we take that England's monarch has been Catholic since the '45, the Church of England is still going to exist. And according to the Church of England (IDK about the Church of Scotland) they don't acknowledge an avuncular marriage. No king of England at that point had married his niece/her uncle, and the 19th century is pretty late for them to start doing so.
Next, let's say that the marriage was not an issue (can't see it happening, but sure). Her uncle/husband was one of the most die-hard reactionaries there was, his most famous comment being about a revolt "I've apprehended the rebels. Send for the hangman". Even if England still/does believe in the Divine Right, IDK if Francesco is going to go over well with most of them. Just consider some of the lyrics to
Rule Britannia in which it contrasts the "freedom" of Britons to "other nations not so blest as thee".
As to a PU between England, Savoy and Modena, there are going to be those in parliament wondering why. Even if Maria Beatrice
is born as OTL, by the time she marries TTL, her father is the king of England, and she the Princess Royal. I can't see anyone in England okaying a match with a comparatively cadet branch of the Austrian imperial family (which is another thing that might be affected by a POD in '45, the d'Estes might still be ruling - Ercole III had two sons, one of whom died in infancy and one who was born of a second morganatic marriage. What's to say that he's succeeded by his daughter, who carried Modena into the house of Austria in the first place? Or that she even survived infancy?). To what end? Is Francesco going to waive his rights to Modena in favour of a cousin/brother in order to marry Maria Beatrice? This isn't like Charlotte of Wales marrying the Prince of Orange - where most Englishmen, even if they didn't like the Dutch, didn't mind it, because, in theory, it wouldn't be a personal union - Charlotte would be queen of England, Orange would become king of the Netherlands, and the inheritance would be split between their kids. Francesco is a die-hard absolutist, he won't abdicate the Modenese throne, and if England believes in a Divine Right of Kings, they're not going to let the inheritance be split. Which means that getting rid of Hannover in '45 is now trumped by their future king having to worry about some duchy in Italy getting invaded by Austria/France (and I'm talking about Savoy not Modena). I mean, I could imagine the English/British feeling that Savoy-Modena is, like Elizabeth said of the Netherlands "your country is a sieve into which mine has extracted little good", that's a figurative albatross/millstone around their neck.