Thank you for all your responses.
I kind of rushed to write that message.
We bought the trailer 2 weeks ago.
2009 Flying Cloud 25FB.
Had to get another vehicle. Our 1997 Tahoe was just not strong enough.
We bought a 2005 Chevrolet Silverado 2500HD.
We had our Prodigy trailer brake controller installed.
The brakes work fine, but I am not sure if it charges the batteries of the trailer. I will read the article somebody mentioned here.
Then, all the outside lights are on on the trailer when it is connected to the truck.
Before we were able to turn the lights on and off by turning off the car's headlights. The daytime running light did not affect it. (we had a 1977 Airstream Argosy before).
When we were camping this weekend the batteries slowly drained.
We were hooked up to a 110V power source.
All 110V power stuff worked, but the batteries did not seem to charge.
We ended up turning off everything in the trailer including the fridge. (The little display uses a little power).
We then drove home. Brakes worked!
Connected the batteries to our battery charger at home and now they are almost full.
The reason I was asking for fuses is that we were worried that a fuse on the converter blew or somewhere else. The ones we can find are all o.k.
At the campground we belatedly checked the polarity and it was wrong when we were plugged in with the 30 Amp plug. That is why we were worried about the converter.
Sorry for the novel.
But that was what happened.