Battery Fuse Blows When Plugged Into Shore Power

You need to find out what device uses the circuit that uses the 20 amp fuse. I don't think it's the converter because it is very small wire, possibly 14 ga.. You could use the same process of elimination that you used previously. Turn off all the breakers, hook to shore power, and with the fuse REMOVED, turn on the main breaker and the breaker for the converter. If that is the fused wire for the converter, you should have measurable voltage above 12v on one side of the fuse holder. If there is no power on the fuse holder, your problem is elsewhere.

I would suspect the fused circuit is for the trailer's emergency braking system. Check to make sure your break away switch doesn't have the pin pulled.