I’m a little confused about your situation. I don’t know the Chrysler wiring, and don’t have a schematic for your car, but in most cases the horn ring provides a ground for the horn, or horn relay. If there was a short in the horn ring it would only provide constant ground and have the horn sounding off constantly.
I also don’t understand what 4 prong switch you are referring to. The ignition switch? It seems to me that your relay is wired wrong. You didn’t mention any of the relay wires going to the horns themselves. I would guess that the H,B,and S on the relay would refer to Horn, Battery, and Switch. If that’s the case, your B terminal is the only one connected properly. S would go up to your horn ring on the steering wheel and H would go to the horns.
Maybe someone has a wire diagram for your car to verify this?