The founding fathers - and the young nation - had just fought a bloody war to separate the states from England under the theory of “consent of the governed.”
To believe the founders wrote and adopted a constitution forbidding peaceful separation of the states just 11 years after the Declaration of Independence is something I would like explained further.
There isn't a necessary contradiction - those who saw the United States as a legitimate nation could favor its separation from England while wanting to maintain America's own integrity. This would certainly have been the position of Federalists like Hamilton.
The Anti-Federalist Democratic Republicans (like Jefferson) would have thought otherwise - but Jefferson played no part in writing the Constitution and probably would have preferred something closer to the Articles of Confederation. Madison, a more moderate Democratic-Republican than the Jeffersonians, was largely responsible for drafting a Constitution that would keep the Federalists happy while at the same time decentralizing power enough to prevent a political revolt from members of his own party.
Our Founders not only believed in "peaceful separation" they practiced it many times, separating large territories into states and large states into smaller ones.
Further, they also "separated" from their old Articles of Confederation -- at pleasure and by mutual consent.
And that is the key to this whole discussion, mutual consent -- where it exists anything is possible, where it doesn't, nothing can be changed by unilateral actions absent some material breech of compact, such as in 1776.
Of course, no such breech existed in 1860.