Something is seriously wrong in your 12V system if it is burning up batteries and converter/chargers. Since it seems to be OK if you just charge while parked, I wonder if the engine alternator could be pumping high voltage DC back into the house system? It may be putting out 15VDC or more and that might be overwhelming the converter, since it is connected to the batteries too. In systems that allow the engine alternator to charge house batteries, there is normally a relay that prevents both converter and alternator from being connected at the same time. Maybe yours has failed? Or you could try adding a diode to the converter output line, preventing any backflow into the converter.
About the only other possibility I can think of is bad AC input to the converter. Or perhaps power from a modified sine inverter, if you have one?
You shouldn't see sparks when hooking up to batteries that are already charged, but may see them if the battery is low.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL