Since the hum in the VHF goes away with the dedicated battery source, that means it is coming in over your power lines not the antenna
line. Hum usually is coming from an AC leak into the DC circuits, or being produced by something else, possibly a florescent light fixture with a bad ballast coil (transformer) in it.
If you have shore power
, physically disconnect it, see if the hum goes away. An inverter
? Disconnect it, see if the hum goes away. Shut down literally half the breakers, see if the hum goes away, if not try the other half. Keep shutting down circuits until it goes away, and the odds are you will be able to find it quickly. Something--a motor
, a pump, a transformer, maybe an electric refrigeration
system?--is making the hum and probably can be stopped with a simple noise
filter added to the offending circuit.
What do you mena by "control circuits attached to the VHF? ? Wouldn't you run that as a separate circuit, directly through one breaker then to the battery switch?