Trailer brakes are not specific to Airstream, so any shop should be able to adjust your brakes. If you take it to a non-Airstream shop, be sure that they know where to properly jack it.
You can do it yourself if you are reasonably handy. The first thing is to remove the brake drums and clean and pack the bearings. While the drum is off, you can determine what way and what tool is required to turn the star wheel to tighten up the brakes. After you put the drum back on, and tighten the star wheel. Look at http://i.b5z.net/i/u/1080235/f/059_045_00.pdf
for instructions from dexter.
If you do it yourself, you don't have to even jack up the trailer. Just run up the joining tire on blocks until the wheel you want to work on is off the ground and go to work.
Hope this helps.