You should spend the 40-60 dollars and install an auto transfer switch.
Here is what I did to my trailer.
(a) Converter hard wired in transfer box to 30 amp generator/shore power with its own fuse. This way converter only comes on when outside power is used.
(b) Inverter power is routed as secondary power source and transfer switch automatically only connects inverter power when generator/shore power is removed and vice-versa. The inverter alternating current will only be available when generator/ac power isn't and the converter will only charge batteries when generator/shore power is available.
Very simple to do and I've done it on a couple of trailers.
ALSO: Don't forget to hard wire with an inline re settable fuse or small fuse panel for your refrigerator AC (alternating current) power. You don't want to accidentally power your fridge by AC that is obtained by inverter power. I know its easy to say, I'll just leave the selector switch on propane and not worry about it, but I've killed my batteries a couple of times by forgetting. I like running the fridge on generator AC when generator is running because it gets colder quicker especially since propane burns much richer at the altitudes I camp at.
I don't use a separate fuse panel for the fridge and converter. Instead, I use separate busman fuse holder outlet plugs for both the fridge and converter. I use a resetable screwable fuse for each so I don't need to carry spare fuses Cooper Bussmann Plug Fuse Holder with Outlet Box Cover Unit-SRU-BC - The Home Depot
Good luck! Autotransfer is worth the small hassle of install.