I would not say that it was as bad as North Korea, but some families were divided by the American Revolution. America and Britain resumed mostly normal relations after the war (though British colonies in the Caribbean did not accept American shipping), so some trade resumed straight away. Diplomats were also immediately exchanged, so there were plenty of channels for people to travel and emigrate.

Many whites who fled to British lines during the war had their property confiscated, and the various local, state, and national authorities never made any serious effort to return these properties or pay loyalists wishing to return after the war. Still, many of these people did slowly trickle back in to the country, even to their old neighborhoods, after the war. They knew, however, to keep their heads down and generally avoided politics.

The only people that really lost permanent access to the United States were those American colonists who took up arms to defend the British, or otherwise aided the British war effort. These people were banned, either by law or by mob rule, from returning to United States after the war. Instead, the British relocated them, for the most part, to Canada. Some, particularly the highest-ranking loyalist soldiers, went to England and petitioned Parliament for reparations. The records of the Loyalist Claims Commission are a great resource for examining the toll the war took on those Americans who felt the Revolution meant anarchy and financial disaster.

Some militant loyalists did find their way back in to America through the Canadian frontier in the early 1800s. By this time, the passage of time had cooled most passions, and the opening of northern and western New York for larger-scale settlement meant that thousands were cutting ties with their past and moving to new places. In this unsettled region, former loyalists could pass themselves off as Canadians or Americans and return.

For blacks, as you might expect, things were harder. Thousands of slaves fled to the British army during the war. Many were resettled to Canada at the end of the war. Some, in perhaps the greatest crime of the conflict, were re-enslaved by British officers and sold to plantations in Jamaica. None could ever return to the United States again, where they would be re-enslaved and returned to their former masters. This made buying the freedom of relatives left behind all but impossible.

Sources: First article in this issue of the Hudson River Valley Review

Maya Jasonoff, Liberty's Exiles

Alan Taylor, The Civil War of 1812.

Not that I know of; remember that relations between the UK and US after the Revolution ended remained at least somewhat polite and cordial(enough for ambassadors to be exchanged and for Jay's Treaty to be concluded). What you do see is Americans who supported the king leaving for Canada and the UK to settle there. The artists John Singleton Copley and Benjamin West for example both settled in the UK although Copley was probably the stronger loyalist of the two and in any case they settled there as much for professional reasons(there was simply more artistic patronage available in the UK) as political reasons and both seem to have maintained fairly substantial ties to the US even after independence. In particular, quite a few Americans traveled to London both before or after the war to study with West and Copley retained interests in real estate in Boston after the war(not to mention his daughter married an American).