When you are driving to and from the parks, what are you running?
My first guess would be that you are running high power things off the house battery with an inverter while you are driving (residential fridge, air cond, etc.). That could substantially drain your battery just on the drive.
Another possibility is a phantom drain. When I had some work done on my engine, the new choke was accidentally hooked into the house battery - it was pulling power 24/7.
Those are both pretty easy to resolve. If they aren't the problem, then I'd look at your converter. It may be that the converter isn't converting the shore power to DC power - so your 12v system is running off the battery even though you're plugged in.
Or your charger isn't charging the battery when you're plugged in. The onboard battery meter will show a full charge when you are on shore power even if the battery is dead. So unplug and immediately check the battery - if it is low as soon as you unplug, then it's not charging properly.