if Im reading correctly OPs campers umbilical cord isn't hard wired, plugs into camper. That's where meltdown occurred, in the incoming receptacle. I can only assume bad physical connection of plug/receptacle or possibly loose faulty wiring at receptacle or plug. Either way, draw of AirCond just caused excessive heat at a bad connection until meltdown.
My thought is though I don't know that campers breaker would come into play on the AC source side? between shore pedestal and camper.
edit 1handyhubby pictures
Scarry part is this is over/in battery compartment?...
Well hope you can make do and enjoy rest of weekend