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His principal objection to unionism was his belief that states have the right to negotiate their own trade agreements with one another and with foreign governments.

No. His main complaints were #1... Agitation against slavery, and #2, the fact that the growing population of the North vs the South and the addition of free states threatened the institution of slavery because slave states were outnumber by free states, even though in 1850, members of Congress did not necessarily vote upon those lines.

You can read Calhoun's last speech in the Senate (which he had Jeff Davis read for him because he was too frail to deliver himself) during the debate of the 1850 Compromise. Calhoun died a few weeks later.

Here's the first paragraph to get you started.

I have, senators, believed from the first that the agitation of the subject of slavery would, if not prevented by some timely and effective measure, end in disunion. Entertaining this opinion, I have, on all proper occasions, endeavored to call the attention of both the two great parties which divided the country to adopt some measure to prevent so great a disaster, but without success. The agitation has been permitted to proceed with almost no attempt to resist it, until it has reached a point when it can no longer be disguised or denied that the Union is in danger. You have thus had forced upon you the greatest and gravest question that can ever come under your consideration: How can the Union be preserved?

Calhoun was right. Just the simple existence of opposition to the institution of slavery was enough to break the Union. That is how tied the power structure in many southern states were to preserving slavery at any cost. They saw any opposition as a mortal threat.