I doubt there would have been reunification. The Confederacy was born out of the demand for State's Rights - slavery was just the issue that ignited the secession. (In retrospect, considering the Socialist tyranny that has since descended upon us, it was probably the right war for the wrong reason.) Knowing the South, slavery would probably have eventually mutated into some sort of system of indentured servitude of both blacks and "lower-class" whites, as a political and economic expedient, since slavery was on the one hand generally a discredited institution in the "civilized" world, but on the other a nevertheless essential element of the South's agricultural economy at the time. But I doubt the people of the Confederate States would have ever tolerated a resumption of subjugation to Federal power, having once won their freedom from it.
The border states and expansion would have to have been given up I'm assuming in your conjecture?
Hard to say... (my crystal ball is in the repair shop). But, with two independent Nations in place of the one, there would have been an ongoing process of various territories and even existing States' swearing (and foreswearing) their allegiances to either one, on an ongoing basis, until the geopolitical boundaries stabilized in some form after the continent was populated.