I'm thinking a second binding might be too thick or stiff if you just sewed it over the first one. I agree with one of the others I just finished a quilt that had lots of issues that I had to redo, etc. When I finally finished it, none of the fabrics that I tried for a binding looked just right. The one that I settled on and actuallly added to this pinwheel quilt doesn't please me bunches but I am done with that one. It's a quilt that was a simple one made with Walmart fabric, it turned out cute but I had to undo and redo some of the quilting, I cut the backing off more than I should have and it barely met the edges, etc. Sometimes it's just better to say this one is done and move on.
B