The First Republic of Denmark-Sweden was thought up after pressures from Vinland and the rest of Europe made people think a republic would be a good idea. Most people weren't willing to fight to far for the idea, and even the most radical believers of a republic didn't want to fight the strong kingdom of the fifteen hundreds.
In the early seventeenth century, however, people believed this idea more and more. Soon enough, protests began in major areas of the state. This wasn't enough to change the kingdom whatsoever, but it was enough to shake it. Over the next year, the protests brought down stablility in the nation, until new protests brought it to it's knees. The kings relinquished their power only after facing execution 1612, four years after the protests officially broke the kingdom.
The republic was a nation which ran on a simple direct democracy. It based it's government off of the New England one, and had a Prime Minister as it's head leader. It stayed out of most world politics, and tried to keep to itself. It was slightly corrupt, as it leaned towards the influence from Vinland to make most of it's decisions. Being like this, it was overthrown in it's Rikardist revolution in 1709.