The Confederacy looked on the War Between the States as a bid to establish itself as an independent nation, equal to the United States in every way. This poem expresses the firm Southern conviction that the seceded states should be allowed to withdraw from the Union in peace and go their own way.
The "broader" stripe refers to the design of the First National flag of the Confederacy, which was patterned after the U.S. flag.
First National flag of the Confederacy (also known as the Stars and Bars)
"Over the River"
This page is http://civilwarpoetry.org/confederate/homefront/river-exp.html
Last modified 16-April-2001