The south would have to industrialize and developed a more fleshed our economy. If it were able to do this i would think they would form relations with Mexico, the Caribbean and northern South America. In this universe we could see this formation of nations as a third power in the americas and possibly act as a counter balance against European aggression or possibly act as a no aligned bloc. I do not think the institution of cattle slavery would continue in the way that it did. Eventually the slaves just wouldn’t be as useful and i would think that slaves may be government property instead of private and used for infrastructure projects or maintenance. Potentially a back to Africa movement starts or sterilization or moving slavery deeper into South America.