On our 2012 Solera "S", I believe we have a combination converter/power distribution center similar to this: Amazon.com: WFCO WF8955PEC 55 Amps Power Center Converter Charger: Automotive
So, I believe the converter is where the fuses and circuit breakers are - on the passenger side of the "house" near the floor - I think under the refrigerator.
Of note, on our "S", the fourth circuit breaker from the top supplies AC power to the converter. Top breaker is 30 amp main, then 15 amp microwave, then 15 amp water heater, then 15 amp converter (+ misc). When my converter didn't run, this breaker was tripped.
From your description, I doubt the problem is your converter. I believe your house batteries should charge while driving - from the vehicle alternator - even if the converter is inoperable.
One thought is the battery isolation circuit - which switches charging of the house battery on and off from the vehicle to protect the vehicle battery from being discharged. Don't know if a fault there would prevent converter charging.
There is, on our "S", a metal cover held on by two thumb screws on the left side of the stairwell. I believe it has a warning to disconnect the house battery before opening. I would check in there for battery isolation fuses.
Alternatively to taking your batteries to an auto parts store to have them tested, if you can get hold of an automotive battery charger, you can remove the step covering your batteries and charge them in place - and see if they will hold a charge. Most "shade tree mechanics" have a charger around the garage or basement.
Good Luck -