I'd say that Richmond. Virginia could become capital given the population increase and industry in the 1800s like in OTL. It was also the capital of the Confederate States of America (CSA) and probably the most important Southern city besides New Orleans, Louisiana, Charleston, South Carolina, Nashville and Memphis, Tennessee respectively.Charleston is currently the capital. Because of the additions of Virginia, Cumberland, and Lower Louisiana plus increased settlement in the territories, Charleston is not going to remain a good fit forever because it’s immediately on the coast and doesn’t represent the increasingly northern and western shifts in population.
As far as what happens to Texas and the Southwestern territories for both America and the Confederacy (the abbreviated name for the Southern American Confederation) believe me not only will Manifest Destiny be very different but so will slavery and how it ends.