Vic, I can tell you how the Trillium
4500 with the original (ancient) converter works because I have exactly the same equipment!
When you are plugged into shore power (110 VAC), the converter should be switched to TRANS, i.e., the 12 VDC transformer is powered on. In shore power/TRANS mode, the fridge should be used in 110 VAC mode, NOT 12 VDC mode. The fridge should be used in 12 VDC mode only when towing.
EDIT: Furthermore, when in shore power/TRANS mode, the 12 VDC transformer is only used to power the 12 VDC interior lights
and other 12 VDC accessories that might have been added to the trailer.