Given the date of the POD it would have to be Hanover wouldn't it??
Have Victoria born male (as it were) or the Hanoverians allow her to carry on being ruler. "British" Hanover is a part of the Empire when Prussia comes calling...
But Hanover and Britain never seemed to have any common political ties to each other than the sovereign. Hanover's concerns dealt with Germany and the European continent while the British were much more global. Not to say the the Viceroy sent to Hanover in the name of the British monarchs, such as the British Prince, the Duke of Cambridge, who served for his father (George III) and his brothers (George IV both as regent and King, and William IV) did not keep in mind British interests. Even George V of Hanover, (The Duke of Cumberlnd) never forgot he was also a Prince of the United Kingdom, but he reigned not for British interests but those of the Kingdom of Hanover. He often made decisions for Hanover as King that were contradictory to his own opinions as a British Prince and member of the House of Lords.
If Victoria were allowed to rule as a woman it might make for a more interesting timeline as her husband Prince Albert dreamed of an Alliance between Prussia and the UK. (He married off his eldest daughter, also named Victoria, to the future Frederick III.). He may have even envisioned a united Germany with his daughter and son in law working together for a more liberal and progressive Germany that he hoped to see.