The Confederacy did NOT want to run "their own little country, within the United States". Total nonsense!
They wanted to completely separate themselves from the United States. They did not want to pay taxes to the Federal Government. Fort Sumter was about collecting tariffs on imports.
In the decade prior to the Secession, the South had managed to pass fugitive slave laws, which meant that any Black person could be enslaved by slave catchers, unless the Black person could show that he had been freed. Since free Black people were not born with papers, this meant that slaves could be held as slaves anywhere in the United States. California was admitted as a free state, but the there was a movement by California senator W.M. Gwin to divide it into two parts, one slave state and another a free state.
The South believed that it had achieved through clever deals and the Supreme Court dominance of the country. Previous presidents like Buchanan and Polk and even Pierce and Fillmore were either pro slavery or anti abolitionists. When Lincoln won with only 39.8% of the vote, they felt they had been cheated, since only Lincoln was sympathetic to abolitionists.
And of course, the South expected war from the very first secession. They WANTED war, because they thought they had all the great generals and the advantage of defending their own territory.
The Southern States were entirely replacing the Federal Government with their own Confederate government. And they started it by firing the first shot as well.
YOU are the one who does not understand history