George I, George II and George III were simultaneously kings of Great Britain and of Hanover, in personal union. I'm aware that the streak ended in 1837 when Victoria became queen of the UK but not of Hanover because of Hanover's different succession law.
During the years of personal union, was any effort made to integrate the two kingdoms? Was any effort made to try to make the succession laws of the two kingdoms more consistent in order to preserve the personal union? Was any effort ever made to incorporate Hanover into the UK the way that Scotland and Ireland had been incorporated?
You would be surprised that early on George I discussed with his advisers how to split the thrones. One idea was to have George abdicate his right to the Hanoverian throne and letting one of his relatives (like a younger son) take over for him. One of the problems with this was that while George I could denounce his claim, he could not do it for any of his children, thus leading to a second set of 'pretenders to the throne' like the Jacobites. Also, the British public constantly brought up the conflicting goals of Britain and Hanover. Hanover was located in central Europe and thus had different potential enemies, and could potentially drag Britain into a war or vice versa. In at least one war, Hanover made peace with the enemy while Britain was still at war with them.
Source: Three Victories and a Defeat: The Rise and Fall of the First British Empire, 1714-1783