OK, now I'm totally confused about what you are trying to accomplish. I thought it was to increase charging current while towing so you cam run the fridge on 12v? But you are saying that's not a problem. There is some kind of basic misunderstanding here I think.
Lets try it this way. Think in terms of energy flows. When you say you want to "top off" the trailer battery once you've parked, where is that energy coming from? Are you idling your tow vehicle and using the alternator to provide it? If so, just change the fridge over to propane and leave the 7 way connector attached. Problem solved.
You can't charge from the tow vehicle without the alt running because that will remove energy from the TV battery and discharge it in short order. If you are thinking that you can charge directly between the two batteries using the 7 way while at the same time charging via an inverter/charger in parallel that won't happen. The dc voltage will be established by the two batteries which are after all connected in parallel forming a single 12V buss. The inverter/charger will just act like a load, basically a high tech heater sucking more energy from the system than its putting back in to the same buss its drawing from. You would have to disconnect the 12V connection between the two batteries and charge only through the inverter/charger. But why do that if you can charge directly far more efficiently just like you are doing while driving?