Sorry but I think that you have it backwards. Ownership of slaves was protected by both the Declaration Of Independence and the US Constitution. But the act of secession was never defined in either document (except rhetorically in the DOI).
The south had the "right" to secede by virtue of the human right to rebel, but what they did and how they did it was extra-legal and the root cause of the Civil War.
Great Britain salivated at the prospect of a US internecine war and stood on the sidelines eager for the opportunity to reestablish control in America. Weakened by the conflict, even had the csa prevailed over the union they would have been ripe for the picking of the brits.
It mandated the return of slaves to the South. It counted slaves as 3/5 of a person in the context of apportionment, a compromise made with the southern states to woo them into the union. Lastly, it outlawed the importation of slaves starting in 1808. These are hardly laws that greatly protected and perpetuated the institution of slavery.
If you want to see the protection of slavery in a constitution, I suggest you read the Confederate States of America constitution where states completely lost the ability to restrict the right to own slaves.