Not only does the War of Independence end early, Canadia and the Bahamas join in too! Disagreements over how to govern and slavery quickly turn the United States of American into an alliance of confederacies. Spain, Britain, and/or France try to gang up on one of the countries during the French Revolution or Napoleonic Wars. The other American countries come to their brother country's aid and realize the need for a united front. They compromise on their differences, and perhaps some make concessions, so that in the end we have the Reunited States of America.
Then out of mirth they invade the British Isles and liberate them with republican freedom. Yay!