[JRTJH]

There is either a 8 pin plug or a series of twist caps that connect your radio to the trailer wiring. Unplug that plug or disconnect the wires (mark them with a piece of tape on BOTH sides of the connector to be sure you reconnect it properly). With the radio completely disconnected you can replace the 15 amp fuse. If it still blows, it's in the wiring if it does not blow, it's in the radio and you probably damaged it when you reversed the battery cables. One or both of the reverse polarity fuses should have blown, are you sure they are both OK? If that system failed to function, that would explain the radio's blowing fuses, but you could also have other damage to control circuits in the water heater, furnace and refrigerator.

I'd remove the radio from the system and see what that 15 amp fuse does.