Let’s say the jacobites won in their 1745 uprising with French assistance and the American revolution ended up happening under somewhat similar circumstances (like taxes being raised after a war the jacobites get involved in but also due to friendlier relations with France causing a proclamation line, the weakening of parliament and equal rights for catholics etc.)
I could see it making the revolution being a pro Hannoverian one because they would be seen as the natural enemy of the jacobite government who were causing the problems for Americans. This could result in an American monarchy under the house of Hannover ruling the new US in a constitutional monarchy (it would be ironic if George III ended up being the first American king). There might be some problems as the potential king might prefer to just rule Hannover so a brother might be sent instead, although the Hannovers would still claim America as part of their claims to Britain so the king of America might also be king of Hannover, maybe sending a king of viceroy there or maybe staying there for some months of the year.) The revolutionaries would also view the old British parliamentary system more favourably since they’d see that as the one that they had prospered under so they might choose a system more similar to that than the more radical system they chose OTL. This would mean no president and senate which means that system wouldn’t be as widespread across the world since the US wouldn’t make it popular, it could also result in the US being more unitary basing their model of the UK of England and Scotland which the jacobites disrupted, but this won’t be too extreme as there’d still be interstate rivalries. Religion would also be impacted since there would be a greater emphasis placed on the protestant identity of the US in contrast to the catholic jacobites and their french allies. This could result in a far less secular America which could encorperate religion into their government in small ways although they aren’t likely to have a national church like the ik due to the religious diversity of protestants in the US. The new nation would also be far less likely to accept catholic immigrants like the Irish and Italians and anti catholic conspiracy theories would be far more popular with people accusing political opponents of being papists far more often. Another effect would be foreign policy related a jacobite UK might be harder to reconcile with after the war meaning hostile relations for longer which would damage trade for the US a lot resulting in a weaker economy and fears of a re conquest (realistic or not) they would also be hostile to France and Spain who the UK would be allied to meaning they couldn’t rely on their alliance, if the UK keeps its part of canada then the US would be surrounded by enemies. This would result in the US being a nation much more interested in its military focusing on building a large army and navy early on rather than having a smaller one a first. Another possibility is powerful and wealthy whig politcal famlies who fled after the Jacobite victory (probably to Hannover) moving to the new US after the war and influencing them to be like pre jacobite Britain.
I could see it making the revolution being a pro Hannoverian one because they would be seen as the natural enemy of the jacobite government who were causing the problems for Americans. This could result in an American monarchy under the house of Hannover ruling the new US in a constitutional monarchy (it would be ironic if George III ended up being the first American king). There might be some problems as the potential king might prefer to just rule Hannover so a brother might be sent instead, although the Hannovers would still claim America as part of their claims to Britain so the king of America might also be king of Hannover, maybe sending a king of viceroy there or maybe staying there for some months of the year.) The revolutionaries would also view the old British parliamentary system more favourably since they’d see that as the one that they had prospered under so they might choose a system more similar to that than the more radical system they chose OTL. This would mean no president and senate which means that system wouldn’t be as widespread across the world since the US wouldn’t make it popular, it could also result in the US being more unitary basing their model of the UK of England and Scotland which the jacobites disrupted, but this won’t be too extreme as there’d still be interstate rivalries. Religion would also be impacted since there would be a greater emphasis placed on the protestant identity of the US in contrast to the catholic jacobites and their french allies. This could result in a far less secular America which could encorperate religion into their government in small ways although they aren’t likely to have a national church like the ik due to the religious diversity of protestants in the US. The new nation would also be far less likely to accept catholic immigrants like the Irish and Italians and anti catholic conspiracy theories would be far more popular with people accusing political opponents of being papists far more often. Another effect would be foreign policy related a jacobite UK might be harder to reconcile with after the war meaning hostile relations for longer which would damage trade for the US a lot resulting in a weaker economy and fears of a re conquest (realistic or not) they would also be hostile to France and Spain who the UK would be allied to meaning they couldn’t rely on their alliance, if the UK keeps its part of canada then the US would be surrounded by enemies. This would result in the US being a nation much more interested in its military focusing on building a large army and navy early on rather than having a smaller one a first. Another possibility is powerful and wealthy whig politcal famlies who fled after the Jacobite victory (probably to Hannover) moving to the new US after the war and influencing them to be like pre jacobite Britain.