In a German-language article on the Danich Kungeloven of 1662 there is an aside about Sophie Amalie von Braunschweig-Calenberg, the wife of King Frederik III. of Denmark-Norway. Apparently she insisted in the prenuptial contract that she would keep all rights to inherit the Welf lands of Brunswick-Lunenburg if the branches of Celle and Calenberg should die out. Brunswick is said to have been one of the few places in Germany where women could inherit the title.
(The source of the claim is Knud Fabricius: Kongeloven, 1920, p. 135. I don't have access to that book.)
Assuming
a) that this correct and
b) it is confirmed/renewed in the inheritance laws for the newly created Kingdom of Hanover in 1815 (as the obvious heiress after the Prince Regent would have been Princess Charlotte),
we would probably end up with Queen Victoria of (the UK&c. and) Hanover in 1837.
How would Königin Viktoria I. govern her distant kingdom? I assume she would not try to abolish the constitution her predecessor William IV. granted. How liberal would Hanover be? What would the political consequences for the rest of Germany be?
I mean, forget 1866, the immediate question is whether she (and Albert - would she attempt to make him king in Hanover?) would she kowtow to the archconservative politics of Metternich and the Federal Assembly in Frankfurt? Small Baden backed off and scrapped its liberal press law when Frankfurt threatened military intervention. Would that work with Vicky and Albert?
Or would the German princes, led by Austria and Prussia, simply assume that Viktoria could not harm them? During the 1830s, there was little respect for the British, AFAIK.