I don't have a full explanation for this map yet, unfortunately, but I'd rather it didn't just sit around rotting on my hard drive, so I'm going to upload it.
The point of divergence centres around the Seven Years War, which goes a bit differently in terms of America. Britain beats France and takes all of New France, including Louisiana west of the Mississippi, which in our timeline was given to Spain. This means that the Acadian French don't flee en mass to Louisiana in the belief that it will remain French, and instead attempt to either return to France, or remain in Acadia.
British policy, however, is to dilute the French Acadian population with English-speaking colonists. This takes place both in a drive to colonise Acadia with British colonists, and in a brutal campaign to drive Acadians out of Acadia and into areas already predominantly English-speaking (primarily the New England colonies and New York).
Instead of diluting possible rebellious sentiments, this spreads the unrest to New England and New York. The region was already unstable due to the imposition of various "Intolerable Acts", but Acadian leaders masterfully add their own expulsion and the massacre of many hundreds of Acadians as another of Britain's many crimes against its colonies. This sparks an earlier American revolution, one where the colonies' populations are much more divided over the issues. Whilst some of the thirteen colonies were considered to be loyal to the British crown in our timeline, in this one no state can be considered to be steadfast in their loyalty; a significant portion of all their populations supports revolution and independence.
The British respond to the revolution in force, and George Washington is appointed by the Continental Congress to lead the Continental Army against their oppressors. Washington makes some early blunders, and is forced to retreat to Virginia to regroup. This is one of the major reasons why he is not considered the almost messianic figure he was in our timeline. This retreat, whilst it was certainly the sanest thing to do in Washington's position, was seen as a slight by the people of Maryland in particular, and the population of all states north of Virginia in general. It was seen as an abandonment of Washington's responsibilities to all the separate states, and this fostered a belief that Washington, as a Virginian, was out to protect Virginia above all others.
Washington's retreat to Virginia was also a blow to the Congress' and France's confidence in his abilities. France was waiting for Washington to prove his worth and win a battle against the British, and therefore show that the Americans could win this war with French help. Washington later advanced and fought an almost phyrric battle against the British forces. It was a victory, if a poor one, and it was enough for France to throw their lot in with the revolutionaries and declare war on Britain.
With France's help the American rebellion had become a war between two great powers, a war that the Americans and the French would go on to win.
What had begun with a riot in Boston had ended with the independence of over half of Britain's American empire. France had gained Louisiana west of the Mississippi back, and the satisfaction of knowing that it had managed to knock Britain down a notch or two.
The newly independent states were far from united, however. Border disputes with each other and with colonies still under Britain's control were common, and occasionally broke out into small conflicts between the militia of the different states. The central government was too weak to do anything to stop the conflict and unite the states. A new constitution was written, but it was rejected by many of the states; it placed too much power in the hands of men they simply could not trust. The Congress ignored the will of the states, and the states ignored the Congress. Chaos reigned.
It became clear that the republican form of government that the Founding Fathers aspired to was either flawed or would simply not work in such an atmosphere of regional conflict.
Another constitution was written, calling for a King to rule the American States. The issue was with who this King was to be; if the American people could not decide on a President to rule them for a few years, they could hardly decide on a King to rule them for the rest of his life. The King could not be an American, as no American could appeal to all states, but then who could he be? That was when a German noble put himself forward for the position.
In our timeline Christian Friedrich Karl Alexander of the House of Hohenzollern had no children, but in this world he did. Christian Alexander died in the mid-1780s, leaving the Margravates of Brandenburg-Ansbach and Brandenburg-Bayreuth to his son, William Augustus.
William was a learned man, with a good head for organisation and a silver tongue that could speak German, Dutch, French and English. He had sold his Margravate to Prussia in 1790, and so had no obligations in Europe. Further still, he was married with a young son; a young son that could be brought up to be a truly American King. As a candidate he seemed perfect, but several state legislatures still rejected the new constitution, that was until William paid them each a visit.
William spoke English with no discernible German accent, and he spoke it fluently. He had been keeping up with developments in the American colonies since the end of the Seven Years War, and was able to quote many of the great men who fostered the revolution. His oratory skills were not always enough to convince everyone that confirming him as King would be in their best interests, but William was a keen political negotiator, and he exploited his knowledge of the different states' histories to make enough promises to convince those last few crucial legislators. The new constitution was passed, and William made the first King of the American States.
William was certainly not a man to sit about idly, and he quickly made good on many of his promises, negotiating treaties between states in order to confirm their borders and even negotiating the Treaty of Albany with Britain, cementing the American States' borders with British North America, most importantly the confirmation of the control of the Ontario area by New York.
Regional rivalries persisted, however, and various voting blocks persisted despite the newly found national unity. Seeing this, William talked with members of the Continental Congress on the possibility of demanding certain frontier territories from the various states, and reforming them as new states. The idea was to balance out the regional blocks, and to create neutral states that belonged to none of them. The idea was approved, and various new states popped up overnight. New York lost the Ontario area, but gained the State of Ontario's legislators and Congressmen as closely-aligned voters. Virginia, North Carolina and Georgia lost various inland territories, but gained Kentucky, Tennessee and Montgomery as allies in Congress. In 1800 the new state of Erie was created, and quickly fell in line with most North-East states in terms of voting.
Now, it is 1801, and interesting events are taking place in France...
To cut a long story short: a different Seven Years War leads to a different American revolution. America's "experiment" in republicanism fails leading to an enlighted, constitutional monarchy, but regional differences persist and all is not well in Europe.
Oh, and you may be wondering about the title; the full term is "The King is dead! Long live the King!", which originally refers to the seamless passage of the title from the deceased King to his heir. In this case "The King is dead!" refers to the ending of British oppression under King George III, and "Long live the King!" is a celebration of King William's enlightened reign.