I think I bent a trailer axle this weekend.  I ruined a tire that had been on the trailer for two years and wearing well.  I replaced it with a new and it blew out before I gone 100 miles.  Same catostraphic destruction of tire as the first failure.  My first impression is that I've bent an axle and it's causing the tires to track funny.

Where do I begin to troubleshoot.  I don't want to put another tire on and ruin it.

Go to the nearest frame/alignment shop and have your trailer checked by professionals. It only takes a couple of degrees from specs by the suspension components, to adversely wear tires and cause damage. In addition to the axle, its mounting could be altered, the wheel run out could be impared, any number of conditions could cause your problem.

This is not an area in which you would want to guess and try to measure by eye. With the knowledge of what exactly is wrong, you can then contact the axle manufacturer for the necessary replacement parts. Once a problem is located, you can then effect a proper repair/replacement.

Yep.  Curbside  Rear tire.

Blew the original tire that had been on there at least two years, wearing normal.  Replaced with a cheap tire because I was in a small one horse town with no choice, and it didn't last 100 miles. Luckily it almost got me home, so I was able to limp home.  I want to buy a good quality tire, but I don't want to put it on, Until I know what caused the replacement tire to blow.