The first thing I would do (and did on the advice of more knowledgeable Forum members) is to do an energy audit on how many AH's are used daily. You can collect this data by using your battery without shore power and measuring standing voltage of the battery before and after (confirming with a hydrometer is also a good idea if you currently have FLA battery).
After tallying the usage, you can interpolate with what you have for charging (or anticipate having) and make a decision as to how much battery capacity you will need. It's better to get somewhat scientific about it rather than make the wrong decision and find that you are low on capacity. Discharging any battery system below the 50% level will mean battery replacement sooner, rather than later. Tongue weight and available mounting locations may influence your decision, as well. Also, you will want to secure your batteries adequately. Installing the batteries in a box and just relying on straps to hold everything in place is a bad idea. The movement of the trailer and loosening of the straps can lead to a really bad situation. TYpically, using a purpose built metal box or steel brackets is where most folks end up.
FWIW, I am a dedicated boondocker using a 120V fridge. My system is set up to run the small fridge for a few days as well as to power all the other devices. I have two battery banks, FLA and AGM, a total of 300 AH. I use a 235W solar module to keep everything charged, both in use and when in storage. The batteries are located inside my trailer near the axle locations in custom built, vented battery boxes. There are a few reasons I chose to do it this way. I am now contemplating increasing battery capacity and solar power to run a small air conditioner. Locations where I camp and upgraded insulation lets me get by with just fans, at present. Anticipating farther destinations makes A/C a good choice for the future. It's all about usage.
Good luck with whatever you choose for battery expansion. It sounds like having an additional 12V battery to aid the cause, at present, may be a better choice than a full upgrade. Best of luck!