Are you running the TV off an inverter? Particularly if it's a MSW inverter, there could be harmonics from the inverter output sneaking into the audio path in the TV. If this is the case, it should be considerably better when operating off of shore power rather than an inverter.
It's also possible that the radio head unit has a hum/buzz regardless of the input presumably due to poor power supply filtering, which may show up primarily when operating off of converter power, particularly if the converter is a ferroresonant converter rather than being based on a switching power supply. Some converters have very poor power output filtering and introduce a good bit of noise in the DC system.
The connection between the TV and the head unit is probably a standard (likely cheap) shielded audio cable with RCA plugs on either end. Sometimes the outer shell on RCA plugs gets loose or corroded and stops making good contact. Squeezing the plug slightly can help restore that contact and may help with the buzz, particularly if it's a new phenomenon.
Long unbalanced audio signal runs are in general a recipe for less than stellar performance, particularly in an area with a good bit of electrical interference around such as an RV. There's a very good reason why professional microphone connections for PA systems are invariably balanced (and line-level signals also usually are balanced). Unfortunately, that's not much help for consumer gear that generally has no balanced inputs or outputs.
