My understanding is 1) the 12.5kw generator supplies power identical to shore power on the 4-prong 50 amp plug. Two of the air conditioners are supplied directly by one of the 50 amp legs, the third air conditioner is supplied directly by the other 50 amp leg. 2) None of the three air conditioners are supplied power through the inverter. 3) Therefore, to operate any of the air conditioners either the generator or shore power must be supplying power. 4) Unless excessive power is being used for other equipment, then one air conditioner can usually be operated when plugged into 30 amp shore power.
It could be that when the inverter is supplying charging power at a high rate, like when the batteries are down some, then there isn't enough power on one 50 amp leg for both air conditioning and the Xantrex. The charging rate on the Xantrex can be limited by programming it to a lower maximum charge rate to prevent excessive demand in this case.
Others here know these systems much better than I do, so someone will correct me also as to my understanding.