Question: Are you trying to run an AC/DC/LP
refrigerator on DC. If so, that is probably the issue. They run on resistance heat in AC and DC mode. DC mode is a battery killer, even if the TV is providing charge voltage to the battery while traveling.
You would do well to buy a few pieces of basic
electrical test equipment. As a trailer owner you will find many uses for them over the years and likely save yourself some money over time.
You at least need the battery hydrometer to test cell condition, but you should also invest in an inexpensive digital volt-ohm meter. You might also consider a basic 12 volt test
light, the kind with an alligator clip on one end and a wire probe (read ice pick thingey) on the other.
The first thing you want to do is check for parasitic loads. With all the switches in the trailer off and disconnected from AC, disconnect the negative post of the battery and put that volt meter between the cable clamp and the post. With everything off, you should read no voltage, with one caveat. Safety equipment, such as CO,
Propane, smoke detectors that run off of the battery are constant voltage drains. Disable these first. If you do have voltage on the negative side of the battery, you have something drawing power somewhere. Start pulling 12 volt fuses, one at a time, until the voltage goes away. That will be the leg where the leakage is, and will localize the problem or further testing.
Some folks try to do this with a 12 volt test
light, but most come with a bulb too strong to find smaller leakages.
Does your trailer have CO,
propane, smoke detectors etc. that are powered by the battery. These are constant drains.
What have you been doing the charge the battery?