Mad King Ludwig of Baden recovers ITTL instead of dying. He marries Princess Alice (Victoria's daughter) and they have a child in 1864 - Prince Leopold, let's say, it sounds a good name for both families. Then Ludwig dies. Naturally, Alice will be Regent, what with her being the child's mother- WRONG. Prince Frederick, Ludwig's younger brother, claims that title. The statesmen of Baden are divided on this matter, and an initial Courtly Dispute descends into a civil war.
Britain, of course, is supportive of Plucky British Princess taking on Evil German Conspiracy, and the level of popular support in Britain prompts Bismarck to support her, hoping to get Britain on his side in any potential match against the Kaiserbund (and possibly to get Baden into the NDU). Unfortunately for Alice, Frederick is pro-Austrian, and has expressed a desire to re-enter Baden into the German Confederation. Imperial France and Austria make it clear that they recognise him as Regent of Baden above all others.
The Regency question strikes a chord in Russia, where Grand Duke Nicholas is acting as Regent for his sickly nephew, Tsar Nicholas II (Alexander II's son). Alexander died a year after taking office, meaning that his ideas for liberal reform have been scrapped, and political dissent is mounting as the Regent seeks to consolidate his power and become the designated heir to the Tsar, at which point it will no doubt emerge that the sickly young man is dead - if he still lives.
One policy on which the Regent has the full support of the Russian people is revenge on Prussia. Bismarck stole Poland from the Rodina, gave it a German King, robbed Russia of her dignity. Any excuse for war will be used without hesitation.
So. France intervenes in the war. Prussia gets pissed. France and Austria and Russia and Saxony invade, each seeking their own grudge match for services rendered. Prussia falls, and signs away what amounts to the Corridor and most of Prussian Saxony, as well as a good chunk of Lower Silesia. Humiliation. Russia annexes Poland again.
Britain invades France before Prussia falls, to prevent an Imbalance of Power on the continent, and begins a slow-but-steady campaign south to Paris, carving a path through Normandy and Picardy to the capital, taking approximately a year and a half. The Emperor is captured, and a ceasefire signed. The British occupiers suppresses radical uprisings, but Napoleon cannot prevent the Empire's downfall, and the re-establishment of a Republic.
In America, the United States and Mexico take advantage of the situation in Europe to kick twenty different kinds of crap out of the Kingdom of Mexico. British forces in the Caribbean happily jump on board this war, aiding a secession in Yucatan and establishing a protectorate over the new republic. The Kingdom is truncated, but does not fall entirely, and the Treaty of Monterrey establishes a Free City of Veracruz, as well as a a general expansion of the USM southwards into Royal Mexico. Yucatan is recognised, much to the disgust of both Mexicos.
