It is interestion that you mention a river that divides and goes in two directions. The Great Divide usually means different rivers. The Rio Grande and the Colorado River both start in the State of Colorado, but one heads southeast and empties in the Bay Of Mexico. The Colorado River goes southwest and empties in the Gulf of California.

The Great Divide in the US is a common name for our Continental Divide which all continents have, exception being Antarctica. It goes the entire length of North America and another one starts when you get to South America.

Since Kate Wolf mentions the direction of rivers in the song, it surely was her inspiration, but I'm sure it has additional implications in the song.