Just to let you know that you aren't being ignored
DW and I have never and will never own a trailer with an outside kitchen (we take a first look and if the TT or 5er has an outside kitchen, we keep walking
), and I, personally, don't know anyone that has one. Can't be of much help.
If you'll post what the refrigerator's make and model is, someone may know or maybe you can "google" the make and model...the manufacturer's website should have the information you need to troubleshoot the power input. There may be a fuse on the refrigerator (an inline fuse) that may be bad or it could be the plug cable is bad. Have you tried unplugging it from the trailer and running an extension cord to it? If it has an internal compartment light, does the light come on when you open the door?
Sorry, I can't be of more help.