Once Arkansas was admitted as a state it enjoyed the same rights and the same privileges as any other state in the Union. I believe that includes the right to withdraw from the Union under proper circumstances. I believe, as James Madison believed, that a state should be able to leave the Union under the same circumstances that a state is allowed to join the Union - with the approval of a majority of the other states as expressed through a vote in both houses of Congress. That is a far cry from the method used by the Southern states in 1860-61, and which was found to be unconstitutional by the Supreme Court in the Texas v. White decision.
Where did Madison say that? Are you interpolating things into one of his 1836 letters again?
The Tenth Amendment governs here, and its language about reserved powers is comprehensive and competent.