Something involving the Children of Queen Victoria would probably work.
Kaiser Wilhelm also becoming King-Emperor of the British Empire is not that ASB.
He was the eldest son of her eldest daughter, and given the rampant inconvenient mortality of European Royalty, he was clearly in the line of succession.
(Victoria's sons were a man who had a permanently reserved suite in a Parisian Brothel, there's a marital aid named for him, who it is a surprise that he did not die young of a social disease, a Professional Soldier whose life could have been ended by a random round on several occasions, and two sons who did pre-decease her. Its not completely implausible.)
Linking Britain and Germany as just close allies would change a lot, having the same Head of State would make it difficult to be active enemies.