Well, I don't see the British forcing an entire state into their sphere. They might take more land, were they completely as devoted to fighting the U.S. as they were to Napeoleon. (Which would take some PODs in Britain as well as the U.S., and probably France.)
Short of really using the South's slaves better than anyone before Lincoln, and probably in a way possible for the period, I also doubt the military victories would be that descisive. I can see the U.S. being forced to conceed territory however, but nothing crippling. (I don't see New England, despite it's protests, suddenly become an English puppet. Or even declaring full independence. Moreover, since the South, at this point, is probably willing to make concessions to keep New England in the war and union if push comes to shove.)
In the end, I can see revanchism being a bigger issue in the U.S. Maybe the abolitionists movement gets butterflied into something lesser, and the U.S. revanchism becomes something more, and Lee is commanding U.S. forces in the U.S.-British war of 1860.
Anyway, Anti-British sentiment in the U.S. was huge in the OTL mid-19th century. Any worse, due to humiliation in 1812, and I suspect another international war before the civil war.