The valance panel bolts to the bumper. The bumper mounts to the car. This link should give you a better idea how they all go together.
Rear Bumper KIt. Fits: 58 Chev Pass Cars
www.autocityclassic.com
If your trying to free up what you have. I say remove the the bumper, disassemble the bumper sections and soak those valance nuts.
Those babies have been on there for for some 65 years most likely.