Battery Fuse Blows When Plugged Into Shore Power

Can you take a picture and post it so we make sure we understand what you are seeing?

What you are describing (yes, the fuse off the battery) is your battery protection fuse. There is no way that fuse (if it really is the battery fuse) should be 20 amps with a 35 amp comverter. It ought to be at least 50 amp, so I think we are confused or you have something seriously wrong with the wiring (you already indicated a previous problem with Refer wiring)