Hanover versus Prussia

Actually, Prussia and Hanover, the latter backed by Britain, nearly did square off in 1729. It seems the Elector of Hanover (George II) was ticked off over Prussian recruiting officers kidnapping Hanoverian subjects for service in Frederick William's army. He threw at least one of the offenders into prison. There was a period of tension then the Prussians backed off and Hanoverian subjects were reasonably safe. I have wondered if this event might have influenced the Prussians to develop a less haphazard means of recruitment by establishing the canton system, which was set up in 1732. As for later, if you look at the run-up to the Seven Years War one of the chief worries of the British government was that Fritz would attack Hanover. The treaty with Russia was intended to prevent that. Fritz advised the French, while still allied to them, to attack Hanover in reply to British provocations at sea and in America. A Prussian-British scrum is a definite possibility, even if it did not actually occur, for it could have, and the possibility influenced diplomatic events.
In the War of the Austrian Succession, 1740-1748, the British and Prussians were actually on opposite sides, though I think they were never formally at war with each other and their armed forces never clashed. The Pragmatic Army that fought the French in Flanders included British, Hanoverian, Dutch and Austrian contingents, while a Franco-Bavarian-Saxon-Prussian coalition beat up the Austrians in Silesia and points south.
The Hessians for example were contracting troops out to everybody it seems: to the Prussians and Austrians in 1744, to the English in 1745-6 (in Scotland, no less), to the Austrians in 1747 and to the Dutch until through the war until 1749.