There are two modern histories of the Nullification Crisis, both of which I think are still in print. Even if not, they're probably accessible in your local library. The more approachable of the two is William Freehling's Prelude to Civil War, which made such a thorough case that slavery was the driving issue and the tariff just a convenient rallying point that I don't know of any serious argument otherwise in the past fifty-odd years. His chapter on constitutional theories ("The Emergence of a Theory, 1828") is hard going but just what you're looking for with regard to state's rights.

Richard Ellis' The Union At Risk isn't a very good history of the crisis on its own, so much as national politics relating to it. He portrays the constitutional issues with only very grudging reference to slavery, but his argument is that Jackson hailed from an older states rights tradition that believed in a permanent Union and South Carolina had adopted a newer one that did not. He's not wrong, necessarily, but there's a lot of talking around the real issue rather than digging in. He's best read as a companion to Freehling.

With regard to Calhoun, his letter to Virgil Maxcy is the best encapsulation of his motives. It's in both books:

I consider the Tariff, but as the occasion, rather than the real cause of the present unhappy state of things. The truth can no longer be disguised, that the peculiar domestick institutions of the Southern States, and the consequent direction which that and her soil and climate have given to her industry, has placed them in regard to taxation and appropriation in opposite relation to the majority of the Union; against the danger of which, if there be no protective power in the reserved rights of the states, they must in the end be forced to rebel, or submit to have ... their domestic institutions exhausted by Colonization and other schemes, and themselves & children reduced to wretchedness. Thus situated, the denial of the right of the state to interfere constitutionally in the last resort, more alarms the thinking than all other causes.

The institution is slavery. Calhoun makes it clear by reference to soil and climate (the environment to grow cotton and rice) and the use of the preferred southern terms: peculiar (meaning special and set apart, not necessarily weird) and domestic (because slaves are imagined to be part of the household) as well as by specifically calling out the South, which is distinguished from the rest of the nation by its practice of slavery.

Freehling also has similar lines from other prominent South Carolinians. It's all in chapter 7, Nullification Victorious. (Freehling doesn't think that South Carolina won, mind. He's describing the moment where the nullifiers in the state turn themselves into a proper, decisive movement.)

For Jackson, the best exposition of his views comes from the man himself. This is his proclamation on nullification.

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