Not enough info for a complete response. Depending on the year of your Sub, the factory alternator may only be 105 amp (even if the build sheet says you have the "heavy duty" electrical package) and won't put out much at idle, so running for 10-15 mins/day probably won't offset drain of the fridge. What kind of battery do you have and what condition is it in? Even with a fresh Grp 31, you are stretching the system's capabilities. Assuming your Sub is a gasser, if it does not have rear A/C, there should be a separate empty battery tray opposite the starting battery, behind the core support. A quick fix for the trip would be to install a second battery there and hardwire it to the other battery, preferably with a big switch to isolate it when necessary. If you do have rear A/C, that tray is already filled with A/C stuff. Before you leave, freeze a bunch of water bottles and load the bottom of the fridge to stabilize interior temps as the fridge is opened and closed, don't just depart for the trip with a bunch stuff that you hope will freeze on the road. Spare battery and jumpers are a good idea, but once that spare battery loses its charge, it will be difficult to recharge with jumpers at idle. I'd take a lithium-ion jumper pack (like a MicroGravity XP10) just to be sure I can start the truck when I have to. Most old computer cords should work for 110V, as long as the connectors match, but remember that newer computers don't draw much current so make sure wire gauge is adequate. The 7.5amp jack might be OK, but I don't know what the max draw is on your fridge. A common mistake with 12V outlets is to use too small a wire gauge when connecting them. Bigger is better, and use an inline fuse.
You are in So Cal, so it will be hot. I just returned from seven days in AZ with a 50L Indel B fridge on the back seat of my truck. Worked like a champ, but I have it wired to a pair of new Grp 34 AGMs with a 270amp alternator. I was driving the truck about two hours per day and that was enough to keep the batteries charged. The day I did not drive the truck, the fridge hit the low voltage cutout after about 38 hours, but the frozen water bottles kept things cool enough for the balance of that day. My guess is that you will have a hard time keeping stuff cold with your current setup. Might want to get a solar setup before you leave. Put insulating blankets over the fridge, even if you have it in a travel bag, and block the rear windows to keep sun off the fridge.
