The states delegated in Article III the authority to resolve disputes between states, or disputes with the federal government to the supreme court as original jurisdiction. When they pretended secession, seized federal property, and opened fire on US troops, they were in violation of that section, and hence in insurrection. By law, the president had authority to determine what part of states were in a state of insurrection.
And the rebels lost. Their appeal to the sword, in defiance of law, morals and custom failed.
Which is exactly right.
If the northern States disputed the definition of property in Article IV Section 2 Clause 3, the should have petitioned the federal government to have it changed.
While they had every right to alter that definition for themselves, they had NONE to do so for any other State, and property belonging to a person in another State should have been returned as such until the abolitionist States followed Constitutional procedures and had the Compact amended. That’s exactly what the Constitution says.
The South was under NO obligation to defend that which had previously been decided by ALL the States. That was supposed to be the federal government’s job.