No, it was not.

Your sibling's probably thinking about the personal union between Great Britain and the Electorate of Hanover. In short, before Queen Anne died without heirs in 1714, Parliament had enacted that the crown would go to her distant relative George Elector of Hanover. (They skipped her half-brother James Stuart "the Old Pretender," due to his being a Roman Catholic.) So, George I and his heirs were simultaneously Elector of Hanover and King of Great Britain. However, the two realms were governed totally separately. What's more, Hanover was only a small part of Germany; it had no influence on the rest of Germany aside from a vote in the Imperial Diet and (after the Holy Roman Empire was replaced by the German Confederation) Federal Assembly.

The personal union finally ended when Queen Victoria took the throne of the United Kingdom of Great Britain and Ireland (as it had been called since 1801). British succession laws followed (and still follow, for the present) male-preference primogeniture, meaning that Victoria could take the throne - even though she was a woman - because she didn't have any brothers. Hanover, however, followed the Salic Law, meaning that no woman could take the throne at all. So, the crown of Hanover went to Victoria's cousin Ernest Augustus - and the Hanoverians were pleased to finally have a ruler living in Hanover once more.