If you stitched your binding on with one row of stitches, when you take that out.... the whole binding will be removed. I guess it depends on exactly how you did the original binding whether just the one side of the binding would come loose. For myself, I think it might be easier & end up with a more pleasing result, if you totally removed the binding & redid it.

Yes, you can just "unsew" the sections where you think you went wrong. I would carefully pick apart the stitches and then carefully hand-baste the binding back on so that you're happy with it before sewing permanently.