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If the motorhome is happy with a normal mains hookup it should be equally happy being supplied by either a generator or an inverter, as long as they are correctly wired and producing the correct voltage.
The only precaution to take would be to ensure no more appliances draw current than the inverter or generator can comfortably supply.
If the inverter is correctly wired and connected and the load is within limits and nothing is happening, the obvious conclusion is the inverter is not producing current.
I suggest you check the inverter is actually working and producing current and if all is good reexamine how it is connected...
u have a bad MW tuner section. this is a transistor radio probably using MW oscillator coils and IF transformers. I suspect the IF transformer or related components cause misalignment hence no audio output from the radio. just noise.