This isn't a particularly complex function. I pass it a couple of graphs and the vertices of the edges that are to become coincident. It appears to work but sometimes the vertex order is changed. Always the duplicated edge is not drawn.
If I extract the EdgeStyle values from the resultant graph and redraw from that data the duplicate edge is drawn but its color is drawn incorrectly.
Can someone point out where I am making an error or what I am failing to comprehend.
Attached the relevant code and results as a pdf.
Just looked at the pdf and realized it might not be as clear as I thought. Here's my method: