A 6A AC draw??? That is huge, resulting in about 70A DC. The modern common res refers like the Samsung (about 19 cu ft) that are being installed are 1A draw and use 100-150Ah in a day when on the inverter. And they run on a MSW inverter which many rigs have. Will your refer even run correctly on MSW if that is what you have?
You will also need extremely heavy wires from your truck alternator to the trailer batteries. IF your alternator can even supply that extra load.
I don't think your refer is practical. But maybe if your 6A figure is not correct.