Your post says, in pertinant part, "and the said United States on their part". This is clearly plural. You also choose to ignore the plain language of Article I.
Furthermore, the Declaration of Indepedence is "The unanimous Declaration of the thirteen united States of America." Clearly indicating that the states veiwed themselves as distinct.
It also says, "That these United Colonies are, and of Right ought to be Free and Independent States; that they are Absolved from all Allegiance to the British Crown, and that all political connection between them and the State of Great Britain, is and ought to be totally dissolved; and that as Free and Independent States, they have full Power to levy War, conclude Peace, contract Alliances, establish Commerce, and to do all other Acts and Things which Independent States may of right do.
Again, independent states. Not part of the United States, but independent states."
From the Articles of Confederation: "Each state retains its sovereignty, freedom and independence, and every Power, Jurisdiction and right, which is not by this confederation expressly delegated to the United States, in Congress assembled."
This clearly indicates that your theory that the states were never soveriegn, independent entities just doesn't hold water.
Historically, your claim is completely inaccurate. It is time to review your preconceived notions in light of solid historical evidence. When you do, I beleive you will have no choice but to concede that the Southern states had a right to leave the union.