The right to stop people from leaving? No, I don't think anyone has that right, or should.
The right to demand reparations? To demand punishment for offenses against them? The right to use force in the Defense against or punishment of others who wronged them? Sure.
But these rights cease once their goals have been met. Anything else goes beyond rights.
So the Southern states had the right to leave. And the rest of the states had the right to sit there and watch them take every bit of federal property they could get they hands on without compensation, walk away from obligations like the federal debt or international obligations, and cut off much of the country from access to the sea via the Mississippi. That doesn't seem fair to me. One side's rights are a lot more attractive than the other side's.
The right to demand reparations? To demand punishment for offenses against them? The right to use force in the Defense against or punishment of others who wronged them? Sure.
And the other side has no right to disagree that there were offenses against them or that the compact had been broken or anything in their own defense. Again, seems like one side has a whole lot better rights than the other side. Must suck to be them.