RV wire color standards don't exist. Yes there are conventions that may/may not be followed unlike homes with standards and inspections. The best way to know is to measure the voltage using frame ground as a reference. You could try the standard household tester and see if the 3 lights are correct. I'll bet a neighbor has one. But it sounds like you have a very small voltage leakage to the outlet which allows the voltmeter to register voltage but appliances don't work. Perhaps there is a tripped CB somewhere.
I'd also guess that your charger doesn't have AC input and hence the batteries die. Did you fully turn off every CB and then fully back on? Are there any CBs on your inverter or charger or charger/inverter depending upon what you have? If so then the same on/off drill.