When you are trying to ask complex questions about systems that are failing, it behooves the inquirer to list even information that he takes for granted that should be known. Example: Is that Girard water heater powered by 12v only, or also by 120V?
In any event, your Magnatek converter is probably at the center of your problems. It may only output 13V or so and leaves the battery constantly undercharged. If you have enough 12V battery capacity and it is all charged, you don't need a converter to make the 12V systems work. Eventually, you would use up that capacity and the batteries would need recharging.
I don't know if your Magnatek is a deck mount model (not inside a multi-function load center) but I'm guessing it is. Bestconverter.com, among other vendors, does sell deck mount converters.
The A/C influencing the heater control panel may be indicative of poor or corroded connections. Without being next to your wiring efforts and circuitry, it's hard to make electrical diagnoses. I'd suggest to get a tradesman with electrical skill to overlook and inspect your trailer and the work you've done. "Neighbor" is not a certification of competence.
