First, the gfci I wil NOT reset unless it has power.
Next question is it tripping or are you just testing it? If it is tripping you have a wiring problem on the outlets (possibly moisture in an outlet).
You didn’t say what the frig is. RV or residential. If it is a RV, then it might be on the GFCI circuit causing you all the grief.
My advice is find someone that can work on it under warranty.
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