There are a couple of things I would try. For electrical problems, a 12V test light and a volt-ohm-meter are very handy, inexpensive tools.
When you say your fridge is left on, if you mean it's fully operational (and not just showing the display) and it's actually refrigerating, that will draw your batteries down very quickly. If that's the case, you can stop reading this post now. Itsbish is right on -- run your fridge off propane when you're not plugged into shore power.
If you mean only the fridge display panel is on and it's not refrigerating, here are 3 diagnostics you might try:
1. I'd suggest disconnecting your ground wire from the battery. Connect the test light between the battery ground terminal and the ground wire. The test light should come on, since your trailer is pulling power. Then I'd pull all the 12V fuses. The light should go out (otherwise you have a simple short in the system). Put the fuses back in one at a time and check the light. If it comes on, make a note of which circuit that is. Pull each fuse back out after you've checked it. When you've gone through all of them, you'll know which circuits are pulling power. As you noted, your 02 sensor will - but it won't pull enough current to drain two good batteries in a few hours. Once you know what circuit(s) might be the problem, you can look for why they're pulling current.
2. Fully charge the batteries, then run a fan for a minute to pull off the surface charge. Then disconnect the batteries from the trailer and from each other. Use a Volt-Ohm-Meter to check the voltage. I'd expect a good, fully-charged battery to read 12.4 - 12.6 V. If you don't have that, you might want to have the battery tested.
3. I've not had this happen to me, but I've read that if you hook up two batteries that have different capacities - even if the only difference is one being significantly older than the other - they can trade current and draw themselves down. There may be better ways to test this, but I'd suggest giving them a full charge, and turning on a fan for a minute to pull the surface charge off them. Then for the battery that has a ground connected to your trailer, disconnect the ground - but leave the two batteries connected to each other. Check the voltage of the batteries. Come back in a day and check the voltage again. If the batteries aren't trading current to draw themselves down, the voltage should be pretty close to what it was when you first checked.