Perhaps you are right. Now substitute the word "secession" for "slavery".
Northern states were not adhering to Article IV, Section 2, Clause 3 of the Constitution ("No Person held to Service or Labour in one State, under the Laws thereof, escaping into another, shall, in Consequence of any Law or Regulation therein, be discharged from such Service or Labour, but shall be delivered up on Claim of the Party to whom such Service or Labour may be due."). That is specifically mandated in the Constitution. How did they get around that?
No, substitute the words "unilateral secession" for slavery. It's quite a different thing. In Article I and Article IV the Constitution lays out a number of actions that a state may not take unilaterally, either alone or in concert with other states, becuase they may affect the interests of other states. The Constitution also requires congressional approval for any changes affecting the status of a state. Whether splitting up, combining with another, or the slightest change in its borders, a state must get congressional approval. Given this, the implication is clear that any action affecting the status of a state, or action which may affect the interests of another state, cannot be done unilaterally. That's where the south violated the Constitution. Secession isn't necessarily a violation of the Constitution, unilateral secession is.