Does the Charger have a grounded plug? Do the other items that you have tried have grounded plugs?Correct...invertor is not connected to AC side in any way, just trailer battery.
The GFCI outlet in the RV is the only thing tripping. If I disconnect the charger I can run other items (heat gun, etc) off this same outlet and it does not pop. The charger is the only thing causing a problem.