I thought I answered this.. My personal belief is the cable is melting due to outside influences (Some heat source other than the cable itself)..
The diagram.. You said, I believe, you have the common wall plate with the 12 volt outlet, switch, LED and antenna jack.
Looking at the back side of this plate, with the 12 volt outlet at the top, there are 3 or 4 cable connections, In order left to right
1: Antenna
2: Cable
3: TV-2
Optional 4: TV-3
(TV-1 is the front jack)
All 2 or 3 TV jacks are hoked to the splitter portion of this device and thus get the same signal.
With the switch on, 12 volts is supplied to the ANTENNA port and that port is selected as the source for the TV's
With the switch off no power goes anywhere other than the accessory outlet at the top of the plate and CABLE is selected as the source for the TV's.
The lead from the park cable inlet goes directly to this plate, no splitters, nothing electronic at all, Straight run.
The antenna lead goes straight to ye-old-batwing, there may (Should) Be a bulkhead connector at the roof line or just under it.
The TV leads go to each TV, ONE of these may be split on some RV's but again nothing that would put power on the leads. Even if it could get past the electronics in the plate.
The park electrician has checked for voltage and fond none (not sure I'd trust his readings but that is paranoid me, And I have my own test gear)
In think the heat source is external to the cable. What else is nearby?
