My question. Why plug in the charger each time you go camping? Leave it plugged in all the time, when you plug in the shore power line to the campground, or at home, or to a generator, it will already be plugged in and ready to charge whatever battery is hooked up to it.
The factory installed "Converter" or charger, unplug it, you do not need it as long as the other one keeps working, until you are ready to trade it in, and then might want to keep the battery charger, just plug in the factory on at that time, and you can take the better one with you.
The solar. It really does not care if the charger is plugged in or not. It will continue to put out the maximum possible amperage until the battery is at 13.2 volts, then it will shut off or go into the standby mode until the battery is low again (such as after you unplug). Once plugged in, the solar normally will shut off - after the battery voltage is above 13.2 volts.
Leave the solar connected all the time too.
Fred.