The first thing I would do is put a Voltmeter on the power wire you used for the Radio.
Measure the D.C. Voltage with the converter off and then on and see what the difference looks like.
I would try a purely resistive load like a lightbulb and see what happens also.
Somewhere the converter is NOT doing exactly what it should if turning it on killed the radio.
If the converter is said to work but will not charge the battery then maybe its regulated output is bad.
loads would tolerate this but more sophisticated loads like the radio might not.
Also maybe it was a coincidence? Try the radio alone straight from the battery and make sure it is fine before connecting it to the converter wiring or better yet,do run a seperate line from the battery,fuse it and connect directly to that.
Again though if the battery is still connected to the converter annd is getting a problematic unregulated charge current it may not be safe to run the radio even when connected to the battery.
Usually a battery will act as a "Filter" to smooth out problems from a converter but that will depend upon how bad the converter is and how good the battery is.
Also I am assuming when you say it was connected to the front lights
that you mean the interior lights
and not any running or turning signals???
Grounding circuits in these trailers is important and tricky too.You need to make sure that you have both a good 12volt positive annd negative connection or odd things can/may happen.