Not sure how yours is set up, but nearly all motorhomes act as you've described. Nearly everything that can possibly be 12V is 12V. Lights, fridge, water pump, etc. Things that absolutely have to be 120V for practical purposes are 120V. Things like air conditioners and, as you've found, 120V outlets.
You have 2 batteries. Typically one is to start the engine and doesn't do much else. The other will be for the "house" - all those previously mentioned 12V things. When the engine is running, it should charge that 2nd battery. When plugged into shore power, a CONVERTER should convert the 120V AC to 12V DC and provide continuous 12V power to your "house" (and charge that 2nd battery).
So....look for a converter and make sure it's working. They're usually protected by a circuit breaker on the 120V side. Look where your power cord enters the RV and follow it to (hopefully) a breaker box and ultimately to a converter. There should also be a 12V fuse panel for the house that you can trace back to a converter somewhere.
