I just think the North and South would hate each other so goddamn much they wouldn't even make attempts to trade with each other, as they would attempt to trade with other agricultural/industrial nations to fuel their own economies.
They wouldn't hate each other given time. Modern sensiblity is to despise the south.
There would be some bitterness but both would privately agree not to get sucked into entangling alliances and go about learning to live next to each other. Both sides would be magnanimous much like they were otl.
The South would not be a pariah state. Once they realised they were becoming one, they'd quietly change policies. They want to be respectable after all. After being snubbed a few times they'll learn.
And considering Queen Victoria's a drug dealer, the Czar massacres Jews, and the Belgians make Nathan Bedford Forrest look like Fredrick Douglas getting up to the standards of the day aren't too hard. The Confederacy might have to up their standards but not that much. They blacks can be residents technically free to make the Europeans happy but still effectively slaves. Yes, some abolitionists will complain but most people change the subject. Many might point to the picture of their dead son in Union blue and say "look what that kind of talk led to."
And after a generation, most people in the North will trade with the south, intermarry the way Canadians and the US citizens do and talk on forums about how boneheaded and immoral Lincoln was to try to bring the Confederacy around by force.
Eventually, that will change but not for a generation or two.
Long term, depending on secondary PODs, the Confederacy can become anything from a Pariah state like South Africa to a reasonably respected second line power like Canada or France in whatever alt NATO came about.