There is absolutely no clause in the constitution that says "Oh, and by the way, you can leave the Union after this such and such...."
Sorry, doesn't exist.
When the state signed the dotted line, they're in it, good, bad, or ugly. The Union does not have an escape button.
That also being said: the confederacy was not a government, it was a group of armed rebels who took over state legislatures and were holding states as territories to be quelled by Federal troops. That statement will cause people's raeglvls to reach new heights, but I'm sorry, I don't, and never will, recognize the "Confederate States of America" as an actual country.
Also: I look at the south like this~
Virginia had one of the largest pulls on American politics as a whole thanks to a combination of it's already massive *It had the largest population by the constitution of 1798* population of free, voting men, and it's slave population, which gave unto it's 3/5th's compromise. The states that profited from this clause lost it due to the non-slave owning population *which turned out o be a lot* moved north to factories and places of industry where jobs were plentiful. It's not our fault that you lost your population due to a shittily-planned, slave-based economy that only profits those born into money, and had a hissy fit over it.... or at least that's what I'd say back then if I was around...