With the RV plugged in to shore power , check the voltage at the fuses.
You should have 13.2>14 volts if the Convertor/Charger is functioning, and I imagine it is , if the lights are operating on shore power.
Then test for the same voltage at the battery.
If you see lower ( only battery voltage) at the battery , then check the voltage in the fuse holder at the trailer end, if you don't have , C/C power there , then you have a second inline fuse or a bad wire between that fuse and the fuse panel.
Are you visually inspecting the fuse , or testing it with an ohm meter?
With fuses; looks good , isn't always good.
99DSDP 3884, Freightliner, XC, CAT 3126B, 300 HP /ALLISON 3060
2000 Caravan toad, Remco & Blue Ox.