The Tacoma will not only run the frig on Battery, but will also recharge the battery while traveling. The length of the drive will determine how much charge is added to the battery.

My propane tank was 3/4 full as I left for the run. I ran AC power 1/4 the time, propane when camped (boon-docking), battery when traveling. The tank lasted a month.

Heater was on only twice to take the chill off, BBQ, hot water & stovetop each day/evening.

Your tank will go for quite a while. I was very pleased to see how long it lasted.

I wouldn't count on the wiring to charge a drained battery to full in a day of towing.  I think of mine more as a battery maintainer than a charger.

You might be fine using the battery while driving.  Worst case your food won't be cold or you might need a jump start once.  After that, you'll use propane!  But, really, if your truck is set up for it, you could be good.  Keep in mind, if you stop for an hour or two either your truck battery could be drained or the power will be cut off to the trailer so your ice cream might melt.

To your original question, I spent a very cold few days in the Smoky Mountains one winter and went through a 20lb bottle of propane in about 2.5 days.  I have a dual tank system now, that switches automatically to the full tank one one gets empty, and, kind of belt-and-suspenders, I have Mopeka.com tank monitors on my tanks, so I can accurately check what's in the tanks on my phone.  Haven't run out since.  Normally, in sane people camping seasons, a 20# bottle of propane will last months.

TT

I guess it's a moot point if the propane option is colder and doesn't use much gas to run the fridge.

Best for us is to use shore (AC) power when available. I don't use the battery for the refrigerator having had one experience when the R-Pod was new of discharging my dual 6V batteries in less than 8 hours. Refrigerator on propane uses very little propane. The stove uses more. The water heater and furnace are the big users of propane. So, to answer your question, it all depends on which appliances you use and how much. There is no set answer as to how long it will last. In the summer, you can expect multiple weeks on one tank. In winter, you may only get a few days if it is bitterly cold outside. I speak from experience here. I've camped in both.

Now, given that it is summer, I would expect your full propane tank to last for the two-week trip unless you are running the water heater a lot for long showers (you would run out of water quickly) or spending all day cooking, neither of which are plausible scenarios. Relax and enjoy your two week trip. If you want to get an idea of how much propane you have left, boil some water and pour it over the side of the propane tank. Wait a few seconds and feel the tank. Above the propane tank will still be warm but it will be cooler where the liquid begins and below.