Could the Southerners have better defended their interests through a political struggle within the Union rather than a military struggle outside the Union?

Considering that the Confederacy lost the Civil War and experienced massive loss of life and destruction of property, yes, they could have better defended their interests by using the existing political mechanisms within the union. War was pretty much the worst possible way to try to defend their interests, as it turned out. Of course, they didn't expect to lose the war. Had they won, they might have been well pleased with the outcome.

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NO, because the interests of the South were diametrically opposed to those of the North. The North was busy with vast industrial entitles, mills putting out shoes, clothes, and other warm garments for cold weather. They had a surplus of munitions. The South had none of these things.

And, most of all, the North had no idea as to the concern of the South over states' rights, which was a major cause of the War. Slavery was not the chief cause, as many wrtings would have us believe. And the tending of cotton fields, in which many of the slaves worked, would soon be coming to a close due to the impending war, with nobody left to tend the fields.

No political struggle within the union obviously could not be resolved, since there was no resolution before the southern states begin seceeding. One after one the states of the deep south seeded and formed the Confederate States of America, with Jefferson Davis as president.