even if we suppose that reasonably likely facts could have played out differently resulting in Lee winning the Civil War, there would have been another, far more devastating war before the 1890s with Southern aristocracy grabbing for California and Nevada.
THAT would have been suicide on the part of the South, and there are legitimate questions as to how economically viable the South was going to be once it gained its independence. Reality was, with the rise of cotton(and tobacco) plantations in many other parts of the British Empire(as well as outside of it) in particular, they probably only had a couple decades before they would have had trouble competing even with slave labor.
The other retrospective aspect on playing that particular alt-history game is the matter of trying to justify a war of Independence vs a war of aggression/expansion. Sure, the US was party to two such wars with Mexico that I can recall off hand, although Texan Independence was only a tertiary involvement item. Their "problem" would be that they had a hard enough time(ultimately failing) getting foreign support during the Civil War. The odds of their getting foreign(--European) aid in an expansionary war approaches 0 rapidly. If for no other reason than there is no real benefit for other nations to get involved(as they could get cotton/tobacco elsewhere). I guess there is a possibility of an "unholy alliance" with Mexico, with very dubious, and dangerous outcomes to be had there in regards to the Monroe Doctrine.
With "reality" having been that the Union eventually regrouped, and ran roughshod over the top of the Confederacy forces after recovering from having its upper echelons gutted by their top shelf generals siding with the South.
All while fighting an offensive war, where the defender has the advantage. You flip that situation around, where the Union has had even just a significant portion of a decade to regroup and fortify its borders against the Confederacy, and the odds for a Confederate offensive war going anywhere positive for them plummet rapidly.
Even trying to do a "proxy war" thing much like what happened with Texas and Mexico doesn't play out particularly well for the South, as they're not rebelling against a tyrannical Santa Anna who evidently wasn't even adhering to Mexican laws in many respects, and dealing with rebellions in numerous other corners of Mexico as well. Throwing in the advent of the railroad and telegraph communications, and the Union also enjoyed a lot more mobility and better communications than Santa Anna could have dreamed of in the 1830's.
What, you think that the USA and CSA could have peacefully split up the rest of the territories when they couldn't even do so under the guise of being one country, with sumners'blood spattered over the Capitol floors, and ethnic cleansing against potential abolitionists in Missouri, Illinois, and bleeding Kansas?
Where did I claim the relationship would be peaceful, or anything close to resembling calm? I simply said that if the Confederacy could have obtained British support, they probably would have won their independence. That doesn't say
anything about what happens after that.
Things would have been very tense(in particular as regards to escaped slaves), there would probably have been no shortage of "incidents" on and along the border. Probably even a concerted effort to try to pull a Texas-like rebellion in some of the US territories near the confederate border. But as far as direct hostilities are concerned, I still stand by saying the South would have been suicidal to launch an offensive war, even with 20-some years to build their own armaments industries and fortifications. The Union simply had too much of a population/industrial advantage at the onset to see that appreciably change.