If you tell us the make and model of 3 way fridge, perhaps we can then direct you to the proper operating instructions for that particular fridge. As
@chartrock has posted, 3 way fridges are not normally connected to the 12 volt van fridge and only are meant to operate that way when connected to tug battery/generating system and engine running to maintain temperatures - not good or recommended for initial cooling or increasing the refrigeration operation.
Operational Priorities are: 1. use 240 volt power when available. 2. use gas when off grid (very efficient). 3. use 12 volt power only when travelling and/or when connected to tug and ENGINE RUNNING. Also, as 3 way fridges draw too much power on 12 volts, not suitable for solar operation even with battery storage as fridge demand for power is always higher than generation by solar and soon runs down battery storage.
Normally the input power line from tug is not only fused, but there are arrangements necessary to disconnect tug from battery power when engine not running - Manual switching, relay switching or voltage sensitive relay. More info if you request same. Cheers.