the only way to blow the battery fuse
would be to overload the inverter
NEVER run a heater on the inverter circuit
what it sounds like is your house batteries are dead, your charge converter { or combo inveter/converter } was supplying all your 12v power, you tripped the CB in your 120v panel for the converter circuit OR blew the DC output fuse on the converter
does your water pump work ? the blower in your LP furnace
try these with the shore power unplugged, and also plugged in
is your fridge still working, it needs 12v for the control board circuit
i'm not familiar with your RV, but our DP has 12v and 120v lights
all the 120v lights are on the inverter output along with the TV etc..
check this out and report back we need the info to help you find your problem