If I turn the DRL's off, the ring around the headlights still stay on

It looks like the DRL and headlight are controlled by the BCM which will need to be reprogrammed to act the way you want it. I know there are people around that might be able to do that like on BMW cars but you will need to look around. Here is the headlight and DRL wiring diagrams so you an see how the system works. Check out the diagrams (below). Please let us know what you find.