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The first thing you should do is look for a shop manual for your year of trailer. I found one one eBay for my '73, but there are several other sources for "official" reproductions. The shop manual will show wiring diagrams for your 12V
, 120V, and tow vehicle umbilical wiring, which I have found to be pretty handy.
You don't want to try and run your airconditioner off of a typical household outlet (15A). Frankly, I am surprised that a breaker didn't trip before you melted your outlet--this may suggest that you have too large of a breaker on that circuit, and you might have ruined wiring in your walls, and have a potential fire waiting to happen. Most everything else in the trailer can be run using the adapter and household outlet, just don't turn everything on at once.
The Univolt is an antiquated piece of hardware. They are noisy and have a tendancy to boil batteries. Call Randy at Bestconverter.com, and he will be able to give you guideance and a fair deal on a new converter.
The univolt is also designed to be used in combination with a battery. If used without the battery, it will still produce 12V
, but rumor has it, that using one without a battery precipitates failure--this might be your problem. Having a meter will definitely help you to troubleshoot.
If your 12V fuse panel is built into the univolt, then yes, you will have to replace your fuse panel when you replace the converter. If your fuse panel is separate, then it is up to you. Personnally, I would replace it just to be able to go with a more modern, automotive style fuse, rather than those old glass ones.