The historical trend has definitely been to emphasize the amount of reconciliation after the war. Many, however, remained bitter, and many soldiers suffered from PTSD and, with very little available to help them, they became violent criminals. Historians like to point to the "Last Reunion of the Blue and the Grey" at the Gettysburg 50th anniversary in 1913, where veterans shook hands and hugged and such. But they overlook the 50th anniversary of Chickamauga, a few months later, where the banquet lunch turned into a bare-knuckle brawl.

The song you are thinking of was written by James Innes Randolph. He was born in Virginia, educated in New York, and during the Civil War held a staff officer position. He was never personally "starved at Point Lookout," as he alleges in the song. He lived in Maryland after the war. While I think the song is instructive in that it reveals the real lingering animosities after the war, it should primarily be taken as a good-natured fight song and not a full-throated diatribe. Confederates, especially Virginians, generally believed that they were the heart and soul of the United States (Jefferson and Washington were Virginians, after all) and that they seceded to protect original liberties. They would not have been anxious to forsake the Declaration of Independence.

It depends on where in the South you were. Secession sentiment was not nearly as universal as is often imagined. Pockets of eastern Tennessee and north Alabama remained staunchly pro-Union, and popular votes on secession cane out against it in Arkansas, North Carolina, and one other state. In Arkansas and North Carolina, the legislatures overruled the voters and eventually seceded. The resentment many Southerners felt was very real and very vicious. However, remember that sources in print were produced by those with resources. Those with resources often harbored the most resentment. If you're interested, Andrew Johnson and Reconstruction by Eric L. McKitrick is dense but really informative.