I don't think there is any way that Prussia will fight a war on Britain's side. Frederick was very bitter with the British for what happened towards the end of the Seven Years War, so he wanted to see Britain humiliated in the ARW. However, he never gave open support to the Americans because it would not accomplish anything.
Also, why would the Prussians intervene for the British if the French attack Hanover? Hanover is ruled by the British monarch, so I don't see why Prussia would feel any obligation to defend it.
Also, why would the Prussians intervene for the British if the French attack Hanover? Hanover is ruled by the British monarch, so I don't see why Prussia would feel any obligation to defend it.