Wasn't the Act of Union at least partially motivated by an English desire to ensure Scotland didn't try to go its own way after Anne's death by selecting a different monarch? Because that's not a factor here.
A brood of kids born and raised in England (rather than the foreign Hanoverians) probably means even less support for later Jacobite attempts to regain the throne (especially if there's also no Act of Union, and less Scottish discontent to feed off).
That butterflies away the highlands rebellions.
As much as I like the Jacobites - and who doesn't love a good lost cause? - this seems an interesting effect. Would there be those foreign powers willing to support a 1715 or 1719 Rising (much less a '45 analogue)?
Removing the Acts of Union completely is unlikely, they'd been in the works since the days of James I, IIRC. It was only in William and Mary-Anne's reign that Scotland was brought to the negotiating table. So we might see a modified Act of Union at a different date to OTL.
Let me throw some famous, possible marriage partners for Anne's children out there:
Charles XII, King of Sweden
George II, Elector of Hanover
Elisabeth Christine of Brunswick-Wolfenbüttel
Frederick William I, King of Prussia
Elizabeth, Empress of Russia
Carl XII - the wildcard. He's proposed for Anne's sister (La Consolatrice), a Polish princess, a Welf princess, a Danish princess - none of which got very far.
But perhaps his dad lives longer or his grandmother forces him to marry sooner (you can't go to war, Carl, until you marry and have a child and heir). However, Anne's Danish husband might see the match foundering on the rocks. Although I do wonder if England wouldn't get involved in the Great Northern War (given Anne's kids Danish connections)?
George II - out. His dad originally wanted a match with him to Carl XII's sister. When that didn't happen, George I let his son choose his own bride - Karoline of Ansbach - since he wanted to avoid a repeat of his own marriage to his cousin. Throw in Anne's hatred of the Hannoverians, and the match seems extraordinarily unlikely.
Elisabeth Christine - the most beautiful princess in Europe and loathe to convert to Catholicism to marry Karl VI. I wouldn't think it impossible that her grandfather - who married his eldest granddaughters off to the most powerful kings in Europe - the emperor, and the second girl to a coin-toss between Carl XII and Alexei, Tsarevich of Russia. So I'd say a match to the prince of Wales is not out of the question.
Friedrich Wilhelm I - Not sure. His mother - a Hannoverian princess - wanted him to marry his cousin. And Friedrich I was so in love with her, he would've walked barefoot to China if she'd asked (she didn't care much for him beyond friendship IIRC). But I'd say it's a possibility.
Elizabeth Petrovna - awkwardly placed. Her father tried for a match to Louis XV that foundered. And according to the bio I've read on James III, before the Old Pretender married his Sobieska wife, he considered Elizabeth. However, the Jacobite court persuaded him, saying that their king deserved far more than a mere bastard (and Elizabeth's parents' marriage was the main problem). Plus, she's born far enough after the POD in 1680s that it's unlikely she'll even be the same person, much less that Marta Skavronski will meet Peter the Great - she might stay a maid in Menshikov's household, or be killed as a casualty of war or whatever.
