Here is a piece of advice that some may find unhelpful. However I believe it is the best thing you could do right now.
Apparently you are not knowledgeable or experienced with working on 12 volt
wiring. There is nothing wrong with this, except that it makes it difficult to utilize long distance troubleshooting help.
You do not need an Airstream Dealer to fix your problem. You simply need someone who is knowledgeable and experienced with Auto or RV wiring to help you.
It looks to me like something is not right with the way the wiring is done in your trailer. There should not be anything wired directly to the battery without a fuse or circuit breaker to protect the wire from the type of damage in your picture.
In my 2010 trailer there is nothing attached directly to the battery posts except the battery cables.
I would strongly suggest that you find someone local to you who can help you figure out what is actually going on.
If you still have your trailer manual, there should be a 12 volt
wiring diagram in it. With that and a knowledgeable helper, you should be able to get this fixed in a very short time.
If necessary, use the jack crank that came with your trailer to operate the jack so you can tow it to any nearby RV or trailer repair place.