Long story short (after ruining 2 sets of marine batteries), I found that the 3 fuses in our converter/inverter device were blown in our LQ.  I replaced the fuses and the test that JAG told me to do showed that it works properly now.

However I want to know how to prevent this from happening in the future and wonder why it happened.  Any thoughts/suggestions?  Do I need some type of surge protector?

I think we may have had a land-line extension cord that had a bad plug or a short in it - we now have one that lights up when its working.  Would that bad cord have blown the fuses? 

Also the stereo system wouldn't work and I had to pull out the unit and replace the fuse in it.  Are these two "blown fuse" problems related?

Why did the fuses blow in these two things but nothing blew in the fuse box?

During hot weather, we keep the trailer hooked up to electricity and I set the AC on 85 to keep things from burning up inside.  I also have a trickle charger hooked up to the batteries to keep them "healthy".  Is this the right thing to do? 

Comments and suggestions will be greatly appreciated as it is really hard for me to "wrap my  head" around understanding trailer AC/DC power! 

Understand these are just my guesses since the only info is your post.

 I think your use of the A/C unit is a likely cause for several reasons.

as the compressor motor cycles on and off it does a couple of electrical flips...

(1) The motor coils as their magnetic fields collapse generate a spike of  voltage.

(2) When the motor starts, it creates a voltage drop.  A small gauge, long or faulty extension cord agravates this voltage drop.  (Always use the heaviest gauge and shortest length cord when you have an A/C unit.).  This voltage drop causes your converter to draw more amps.  Maybe enough to trip the over current device (fuse or circuit breaker)

The trickle charger is in addition to your converter?  Why doesn't your converter keep the batteries charged.  This could also be a cause of your problems.  Two separate devices, unless they were designed to work together, putting power to the same circuit is an invitation to trouble .

Thanks for your reply.

I no longer need the trickle charger since the converter fuses were replaced.  Since our batteries weren't staying charged, I got the trickle charger to keep them boosted.  Otherwise just sitting there they wore down.

I have a RV extension cord and its plugged into an RV connection on our power pole.

So if I'm running the AC I'm liable to blow the fuses again?   

How long and what gauge is your extension cord?

The cord will be imprinted with some numbers & letters signifying the gauge and type.