Replacement Battery

Get a digital voltmeter if you don't already have one. Is the battery flooded? If so, be sure that the plates are covered, using distilled water only. Leave the battery on the charger and the trailer plugged in for a few days. Disconnect the battery (-) terminal. Wait an hour, then measure the voltage. It should be around 12.6-12.8 volts. If its low , then next would be a discharge test. If its lower than that voltage then it probably has a bad cell and needs to be replaced.

For the discharge test you will need to put a load with a known current in amps on the battery for a known length of time so yo're taking out about 50 amphours (about 50% of the battery capacity rating). Let's come back to that once we get through the first step. 

Look for causes that might be an excess load. Check things like the pin in the safety disconnect switch. Check that there is nothing turned on, to include the refrigerator on DC power instead of propane. Check the antenna booster (although that would not explain an overnight drop that bad). Are you running an inverter for anything?

Just to note, even if a battery is not that old, it can develop a fault. I've had car batteries last only a year or two. If you can get the battery tested, do so. If that is the original battery, it is a dual-purpose battery, not a true deep cycle battery. It sounds to me like you need a setup with one 12V deep cycle battery or two 6V GC2 batteries in series,  or as in my case, a LiFePO4 battery (but that requires a lot more changes to get it going).