Generally 12 volt will not cause 120 volt issues save for those devices that use 12 volt for CONTROL power.. Fridge, Water heater, A/C(s) all use 12 volt for CONTROL power.
IF you have an Intelletec EMS it may also use 12 volt (Do not know) this is load shedder measures the current in the neutral line and if you are on 30 amps will turn an A/C or selected other loads on or off to keep it below 30 amps.
Progressive Industries EMS is a totally different animal. it will cut off 120vac to your RV if it is not close enough to 120V and 60Hz.. This is a good thign.
But it sounds like your converter may be flakey as well.
Oh and you said 4 G-24's that's about 300 amp hours of battery
IF YOU HAVE THE HEADROOM (they are taller) use of 4 GC-2 (About the same price) gives you 440 Amp Hours and TRUE Deep Cycle (whqt you have now is really a starting battery) that's nearly 50 percent more power and over 100% more usable power and no additional cost. Just move a few wires about (Since the GC-2 is 6 Volt.) Think about it.
