Re: 12 Volt Battery Choice
I'm wondering if it's a short to ground that might be the cause? If you have an ohm meter, disconnect the battery & 110V supply, touch the ends together (discharge any capacitors), then check for continuity from the positive wire to a ground point (bumper). There should be 0 ohms. Repeat as you turn individual switches on in the trailer. Worth a try!
Also, take the battery to a mechanic shop & have them do a load test on it. That will tell you if it's the battery , or not.