As far as the U.S. Civil War goes, I think it would be hard to justify the position that the South had a moral right to secede, but that the slaves did not have a right to rise up in rebellion against the system of slavery. I rather doubt that the Confederates would have agreed with that, though. Admittedly, the slaves hadn’t, by and large, shown much inclination to mass uprising, and Southern apologists for slavery would have probably argued that the second case was absurd, because slavery benefitted both whites and “Negroes”, and the slaves had no reason or desire to revolt, except when they were being misled by wicked Northern propagandists, and so on. I don’t know what the racial dynamics of an independent, aggresively pro-slavery Confederacy would have been. Possibly very ugly.
As to modern secession movements: Actually, the United States has–for very good reason, because there really isn’t a good place to draw the line–been pretty reluctant to recognize breakaway nations. We haven’t recognized Chechnya, for example, nor Tibet (despite all those bumper stickers). East Timor was something of a technicality: arguably, Indonesia’s occupation was illegitimate to start with, so that situation was one of one country invading another country, rather than part of one country seeking independence. (Also, the U.S. actually didn’t do jack for the East Timorese, but rather supported the Indonesian government; we recognize them now because the reality on the ground is that they are independent, which even Indonesia now acknowledges.) In the case of Eritrea, we again recognized something formally acknowledged by both parties. What happened there was that the Eritrean independence movement formed an alliance with anti-government rebels in Ethiopia proper; when the rebel coalition overthrew the old Ethiopian regime, the new Ethiopian government was willing to recognize the independence of their then-friends, the Eritrean nationalists. For us to insist that Eritrea or East Timor were still parts of their old motherlands, when the governments of Ethiopia or Indonesia no longer claimed them, would be pretty silly. As to Taiwan, we never recognized Taiwan as a breakaway new state; rather, we recognized the Nationalist government on Taiwan as the legitimate government of all China. When we established diplomatic ties with the People’s Republic, we severed formal ties with Taiwan. Our official position is still that Taiwan is part of China. In the case of the former Soviet republics, we were actually pretty far behind the curve–George Bush (the elder) was widely seen as being very cautious about the breakup of the Soviet Union. Again, we eventually recognized the facts on the ground, because the U.S.S.R. simply ceased to exist. (The Baltic States were something of a special case since we’d never recognized their incorporation into the U.S.S.R., making them legally more like East Timor in that regard.) Many would argue that both the (elder) Bush and Clinton administrations, whatever rhetoric the latter may have used, were actually very slow to take action in the former Yugoslavia. Again, at some point it was self-evident that the old Yugoslavia just wasn’t there any more. I have seen criticisms of the European and American decision for early recognition of Croatia and Bosnia-Herzegovina; once those republics were recognized, though, then diplomatically speaking it wasn’t a civil war anymore, it was a trans-border international conflict. The argument for early recognition probably would have been that, again, the old Yugoslavia had already de facto collapsed. We still haven’t formally proclaimed recognition of independence for Kosovo, whatever the facts on the ground may be.
I think there’s also a difference between breaking up a country, and the situation with African and Asian de-colonization after World War II, where distant colonies declared themselves independent from countries thousands of miles away, to which they had no real historical or cultural connection, and where the imperial powers wasn’t even claiming that the colonies were part of their unified, sovereign territories. The American colonies did of course have a historical and cultural connection to Great Britain, but they weren’t really legally considered part of a united state, the way England, Scotland, Wales, and Northern Ireland are; rather, they were more or less autonomous “dependencies”.