First question would be: what kind of battery is it, deep cycle or starter battery.
Second Question: How many Amp/h capacity (only ~50% of what the label says is usable)
Third Question: What are you trying to run when dry camping?
You're loosing at least 25 Amp per day for your LP Gas detector, CO detector, smoke alarm, system monitor, thermostat.
You also need electricity for water pump, lights, radio, tv, maybe the furnace kicks in a few times, you get the idea.
If this battery came with the trailer I bet it wasn't the most expensive one they had available, so lets say a 12 Volt Marine type battery with 100 Amp/h capacity. That leaves you with ~40 Amp/h to burn, which is nothing for dry camping. The next problem is when these type of batteries are being discharged to often to far down they will die prematurely plus the converter/charger in the trailer might not have the power and or the time to charge it to 100%.
What you want is at least 2 true deep cycle batteries like 6 Volt golf cart batteries or good 12 Volt deep cycle batteries with a minimum of 200 Amp/h nominal capacity for a weekend.
Edit: I almost forgot, check how many Amps are being drawn from the batteries using an Amp meter and then do the math.
2013 RAM 3500 Dually Longhorn
2014 Trilogy 3650RL, W/D, Onan 5500, 8000# Axles, IS, 960 Watt Solar, 6x6 Volt Battery Bank, Freedom SW 3012 Inv/Charger