Ok, so lets start building a timeline here. The Point of Divergence is that Alexander Hamilton moves to Boston instead of New York City. This puts him firmly among the intellectual elite of the city, becoming a student of people more like Samuel Adams and John Adams than William Livingstone. He would become a close friend of George Washington and an avid Federalist. He would write the famous Federalist Papers, which would circulate around Massachusetts in the lead up to the Constitutional Convention of 1787.
At the convention, delegations from all of the thirteen now free colonies except for Rhode Island would arrive to discuss the issues of the Articles of Confederation and how to fix them with a new Constitution of the United States of America. The US Constitution that we all know is what exists this convention, it is ratified by Delaware, Pennsylvania, New Jersey, Georgia, Connecticut, Massachusetts, Maryland, and South Carolina by May of 1788. New Hampshire, New York, Virginia, North Carolina, and Rhode Island all refuse to ratify the Constitution, seeing it as overly Federalist. While the states that ratified the Constitution anxiously wait for one of them to break, New Hampshire, New York, Virginia, North Carolina, and Rhode Island are avidly anti-Federalist and continue to only recognize the authority of the Articles of Confederation. Accepting the Constitution is debated and voted on in the state legislatures of New York and Virginia, with both votes failing. Rhode Island and New Hampshire don't even vote on it, with the opinion so overwhelmingly against "Hamilton and Madison's new government order."
North Carolina is far more divided than the rest. While popular sentiment is anti-Federalist, there are strong elements of Federalists among the state legislature. After much heated debate and a close vote, the state votes to ratify the Constitution in September of 1789, over a year after the other Constitutional states joined. The states that are still under the Articles of Confederation show open contempt for the Constitution and clearly will not join. Their strong anti-Federalist rhetoric is popular and causes a near revolt in western North Carolina. Confederation Representative George Clinton called what happened in North Carolina "a subversion of democracy" and called for a reversal of the decision. As protests and riots broke out all across the state, North Carolina Governor Samuel Johnston brokers a deal with David Caldwell, a representative from western North Carolina and anti-Federalist leader, and Alexander Martin, the chosen representative of North Carolina for the Constitutional Convention. The solution they arrived at was to divide North Carolina in two, with the eight western counties of Rutherford, Burke, Wilkes, Surry, Rowan, Lincoln, Guilford, and Randolph breaking away to form a new state, the State of Franklin and having David Caldwell serve as its first governor. Franklin was officially admitted into the Confederation Congress in March of 1790, defusing the situation for now and avoiding any kind of national crisis.
There are now nine Constitutional States, Delaware, Pennsylvania, New Jersey, Georgia, Connecticut, Massachusetts, Maryland, South Carolina, and North Carolina, and five Confederation States, New York, Virginia, Rhode Island, New Hampshire, and Franklin. Tensions are high and will get even worse during the first election for President of the United States since the adoption of the Constitution by most of the states.
EDIT:
For those unfamiliar with the county map of North Carolina in the late 1700s:
http://www.usgwarchives.net/maps/northcarolina/statemap/1780NCCounties.jpg