Your entire argument is highly flawed because you missed one logical point:
Would the states have joined a union in which the central government would dictate to them the way our federal government does today by forcing rules and regulations, and huge taxes on them?
Thus, the representation of the union was different than the reality of it today.
The states entered into a union in which they expected to have great control over and states rights, but that is no longer the case.
Because the union is not working the way it was represented at the time of its establishment, the States have the natural right to remove themselves from this union, and reenter it if they so desire, with a new agreement between them and the federal government.
I offer supporting evidence from our own Congress:
This read is well worth the time it takes:
In every stage of these Oppressions We have Petitioned for Redress in the most humble terms: Our repeated Petitions have been answered only by repeated injury. A Prince whose character is thus marked by every act which may define a Tyrant, is unfit to be the ruler of a free people.
Nor have We been wanting in attentions to our Brittish brethren. We have warned them from time to time of attempts by their legislature to extend an unwarrantable jurisdiction over us. We have reminded them of the circumstances of our emigration and settlement here. We have appealed to their native justice and magnanimity, and we have conjured them by the ties of our common kindred to disavow these usurpations, which, would inevitably interrupt our connections and correspondence. They too have been deaf to the voice of justice and of consanguinity. We must, therefore, acquiesce in the necessity, which denounces our Separation, and hold them, as we hold the rest of mankind, Enemies in War, in Peace Friends.
We, therefore, the Representatives of the united States of America, in General Congress, Assembled, appealing to the Supreme Judge of the world for the rectitude of our intentions, do, in the Name, and by Authority of the good People of these Colonies, solemnly publish and declare, 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. And for the support of this Declaration, with a firm reliance on the protection of divine Providence, we mutually pledge to each other our Lives, our Fortunes and our sacred Honor.
All but one of your arguments are based on the current state of the Union, and have nothing to do with Lincoln and the Civil War.
However: Because the union is not working the way it was represented at the time of its establishment, the States have the natural right to remove themselves from this union, and reenter it if they so desire, with a new agreement between them and the federal government.
No. This is wrong.
States do not operate under "natural rights," but under the Constitution. Article VI makes clear that they cannot simply remove themselves from the Union at will.
The states explicitly do not have a right to enter (or re-enter) "if they so desire." They can petition Congress to be admitted. Congress is empowered to define the conditions of entry, and to deny re-entry on whatever grounds Congress may choose.
Finally, you quote from the Declaration of Independence, which states that the colonies could break away from the British crown for just cause. The cause for secession was primarily the South's desire to maintain slavery. Not much "just cause" there.
I note one thing, however: I don't recall ever seeing any case where the Southern states ever attempted to formally remove themselves from the Union in a legal fashion. Perhaps they did, and I'm simply unaware of the fact. Instead, they just up and left.
Unlike the Declaration, the South seems not to have exhausted all options, but instead chose to incite a war.
Which is arguably because the States have been negligent and derelict in regard to their duty.
...the States have the natural right...
I was unaware that States have natural rights.
... to remove themselves from this union, ...
I don't see that they have a right to remove themselves from the union on the basis that the union is not working the way it is supposed to when they have contributed to that situation in regard to a Perpetual Union they agreed to form.
... and reenter it if they so desire,with a new agreement between them and the federal government.
Why would there need to be an ageement between them and the federal government? How could there be? The United States and the Federal Government are not the same thing. The Federal Government is not the first government the United States has had. If the Federal Government was to be involved (assuming it even existed at such a time) wouldn't it merely be acting as an agent and on behalf of the States united?
I offer supporting evidence from our own Congress:
"Our own Congress" is a stretch. That's from the First Continental Congress which I don't see to be the same as the Congress we have under the Federal Government. That's at least two Governmental reorganization's ago isn't it? I'm not disparaging the Declaration Of Independence though.