It would be helpful to know something about your motorhome. Gas or diesel, year, make, model.
Always use true deep cycle batteries for your house 12V system. Starting batteries are not designed for the constant discharge/recharge cycling. If you already have two 6 volt batteries (deep cycle golf car batteries) I would add two more (since they have to be wired in series creating a 12V pair).
Four good 6volt golf car batteries wired properly to create two 12V pairs should run your fridge just fine. When you are driving down the road, your engine alternator should be charging the house batteries so running the fridge on the inverter should be no issue. When you are parked, the inverter will power the fridge until the batteries get low. Running the generator for a couple of hours at night should keep them charged.