But, IF a State like Kentucky had the right to declare itself "Neutral" in 1861, and the Federal (Lincoln) Government reconized that right to some extent in that they were extending help to the Unionist in Kentucky in violation of that Neutrality, how did a State NOT have the right to Seceed if it wished to.

It is the nullification arguement that has recently arisen again that the states have the right to refuse to obey, or impliment, an illegal or unconstitutional federal law. The same as a soldier has a duty to not obey an illegal order that his officers may give him.