What if the British had done slightly better in the American Independence War - not enough to keep control of all the colonies, but some of them. See, I've heard that at one point the French considered offering a peace deal which gave the British South Carolina, Georgia, the northern parts of Maine and New York City.
So what if thiss peace had gone through? How does the absence of much of the south affect the US? Would later wars take place between the two and if they do would it be Britain trying to retake control of the US or the US trying to annex British territories?