With the RV converter charging the battery by being connected to shore power, your external battery charger should signal that the battery is fully charged and most will shut down unless it's a very old type or a real cheap basic charger. I'm assuming the converter charger is working and if so should charge the battery by itself. Then the external old etc charger will just be connected with no additional charging amps going to the RV battery because it thinks the battery doesn't need any charging and won't accept any amps. Chargers vary greatly and over the years of being made.
To charge an RV battery when the RV is connected to shore power, take the + (red, positive) cable completely off the battery's terminal to be externally charged and at least wrap a dry rag around the cable end to insulate it so it can't short out by bumping into against anything. It will be a very high amperage spark if shorted out and if battery acid gasses are present in dense enough concentration, there could even be an explosion happen and acid thrown all over you. After charging the battery, reconnect the cable tightly. Not smart to have dual charging sources connected to a 12V etc storage battery at the same time as many things could happen and few are good things.
