There is no reason at this point to think that you haven't fixed your battery discharge problem. Go ahead and reconnect your battery and recharge it fully, then disconnect from shore power. Do that early in the day and monitor its status over the course of the day, just to be sure that you haven't missed anything. And do disconnect it or leave it on shore power while stored, as others have said there are some "phantom" loads you can't otherwise get rid of that will discharge your battery over time.

On to the brakes. Yes, there is quite possibly damage there if you drove very far with them engaged. As trailer brakes are a critical safety system it needs to be checked out before any more travel. Are there signs of overheating? Burned paint on the drums? Smoke or smell while you were driving home? If yes then pull the drums, do a brake inspection and bearing repack. 

If there's nothing obvious then reconnect the trailer and brake controller and go to an empty parking lot. Test the trailer brakes by rolling through the lot at about 5 mph and engaging the manual slide of the brake controller so that you're stopping your rig with trailer brakes only. Does the rig stop smoothly? No grabbing or strange noises? If that checks out then find an empty roadway where you can drive at around 30-40 mph and do the same manual stop a couple of times. Then pull off and see if both brake drums are hot (they should be hot from stopping the rig but not smoking hot) to the touch. 

If that checks out you're probably OK for the moment, but I would still be pulling the drums, doing a full brake inspection, and repacking wheel bearings before making any longer trips. 

Hello and welcome!

Two things are happening. First is that lead-acid batteries self-discharge even if nothing is drawing power. That would take some time though since you say it seems to be happening quickly.

Second is that there are always power draws. This can't be helped. First is that there is the CO/LP detector. It is hard-wired in so it can't be disconnected. That is a safety thing. Have you checked the booster for the TV antenna? Make sure that is switched off as it will draw power when turned on. The thermostat and refrigerator panel also draw a small amount of current, even when turned off. There are probably others I have not mentioned. Since yours is a 2016 (same as mine), I know it did not come with USB outlets unless you installed them. You already said your refrigerator was turned completely off. It is hard to imagine anything with sufficient power drain that would kill a good battery overnight if everything possible is truely shut off.

You could leave the RPod plugged in to an outlet. 15A will do if all you want to do is let the converter keep the battery charged. If that is not possible, then you either need to disconnect the negative terminal on the battery or install a battery cut-off switch so that the battery can be completely disconnected. Other steps you can take are to go to the DC side of your converter (charge the battery first). Pull the DC fuses. Check to see if pulling the fuses eliminates any power drains. It helps to have a clamp-on DC ammeter. One at a time, replace fuses in their original locations. If you see the meter jump to a higher power use when you do so, you will narrow down places/items to check.

I hope you can figure this out. It must be frustrating, not to mention expensive to have to replace batteries. If you have been letting the RPod sit with the battery connected for any length of time and the battery did run down, you may charge it but it may not be holding a charge. A very deep discharge can damage a battery. Any time it will be sitting unattended and without being plugged in, the battery needs to be disconnected, either with a cut-off switch or by removing the negative terminal (for safety and to avoid possibly making huge sparks.

Actually, everything is not off.  The radio/clock, CO/propane detector and the 'fridge controls are always on.  I have a battery disconnect switch and that is enough to protect the battery from full discharge.  I also have a 25 watt solar panel and charge controller to prevent the battery from self-discharging. 

https://www.amazon.com/Battery-Tender-021-1162-Charger-Controller/dp/B004Q820UK

https://www.amazon.com/ECO-WORTHY-Solar-Panel-Module-Charging/dp/B01IFJ73X4

https://www.amazon.com/Battery-Tender-081-0069-6-Terminal-Disconnect/dp/B000NCOKZQ

I suspect the panel is enough to keep the battery up with all of the dark current on, but I haven't tested it. 

The electric switch on your actual water heater is 110 only, so that should not be a factor.

My first thought is that you have a short somewhere in the system between your battery and the converter.

I am sure someone with more knowledge of the systems will jump on here soon,