As the title says, you guys need to propose situations in which the USA and the UK, unite economically, politically and, militarily. Posting this in Post 1900 as well. Bonus points if, well, you achieve this at all, as it seems a little ASB to me...
Perhaps a Brazil like situation could work?
America rebels, the British are able to put down the rebellion but settle for the creation of an American parliament to prevent further conflict.