Lee with everything he wanted would have been unstoppable, but the only chance the south really ever had would have been to get into Washington early, while the people were still overwhelmingly pro-south, arrest Lincoln, fly their flag, etc.
Bickering among the southerners would have broken out more along regional lines than state by state. Plantation owners of the Atlantic seaboard and east Texas had ideas about things that were not popular with uplanders and city people. This was evident even during what we call the War of 1812, really just a sideshow of the Napoleonic wars. New Englanders were almost pro-British, but the farther south you went, the more attractive was the idea of exploiting British weakness to secure Mexico and Cuba.
If Richmond had succeeded in setting up a new nation, I still think regional concerns would have prevailed. After a cooling-off period, Mississippi Valley people would have realized their bread was buttered in the upper plains and Ohio and Virginians would have craved trade with Maryland and Pennsylvania. The deep south might have been a problem. They may well have decided that European connections would help them establish new plantations in Mexico and Cuba. This may have led to a second Civil War, which South Carolina would have lost spectacularly.