How would the survival of Queen Anne's son, William, Duke of Gloucester (and his production of issue, male and legitimate) affect the fortunes of the house of Stuart? I've read that the Jacobite risings were caused in part because James III was a nearer relation to the last king (Anne) than George I was and therefore was the rightful monarch.
But, if William succeeds as William IV, King of England, France, Scotland & Ireland (assuming that the Act of Settlement and Act of Union do not get passed, since they were passed after his OTL death), then by the law of proximity of blood, he is then a nearer relation than James - son versus brother.
Any thoughts on how the Jacobite movement might progress under a half-Stuart king rather than a complete foreigner? Would the Jacobite movement even develop?