First, what refrigerator do you have? powered mobile cooler/freezer is pretty vauge.
Don't run it off AC power unless you are plugged into shoreline/generator. Using an inverter to run it is less efficient than straight off DC.
I agree, if you will be away from shoreline power rarely then just run this off of the house batteries (or add to house batteries).
If you want a new battery system then it is no different from your current battery system. Charging source - batteries - outlet.
I would really consider a roof solar rather than the portable.
Mount the battery close to the fridge. Run the fridge to the battery to get power. Super easy.
For charging use a solar charge controller connected to your new solar panel.
Also, connect it to the vehicle alternator for when you drive. Use a solenoid switch so it is electrically connected to the alternator/starting battery when the motor is running and when ignition is off the switch turns off. Hint, you can use the radio ignition power feed to tell the solenoid switch when the vehicle is on/off.
For charging off of shoreline you can put a switch to connect it to the coach batteries that are being charged, or you can add a new charger just for your fridge battery, and when it is powered from shoreline it will charge.
