Scarlett is attempting to be a proper, refined Southern lady in the pattern of her mother while indicating to Rhett that she is unhappy with him. The phrase isn't an obscure southern expression - it's Scarlett's method of cleaning up what she'd really like to say at those points, which would be to tell Rhett to "go to hell." She uses the name Halifax only because it sounds similar to the word she would prefer to be using, since they both start with "h" and quickly follow with the "l" sound.

Any other place name with similar sounds would have worked just as well, but there was a Halifax in Virginia, one in North Caroling, and one in Florida, so she was aware of these places and adopted that location for her phrase.