First, if you have not purchased an inverter, buy one with an automatic transfer switch built in. Without those other loads, you probably only about 1000W inverter so checkout a
Samlex Inverter/Chrager/Transfer SwitchSecond, you are correct about requiring a fuse/breaker AFTER the inverter !
THIS IS PROBABLY NOT CODE COMPLIANT, BUT THIS IS WHAT I WOULD DO.
Get a 240V
fused A/C disconnect box. Run the hot from the shore power plug to one of the input of one of the fuses. Split the output of that fuse and run one of the wires to the hot inut of the inverter/charger/transfer box and the other to the non-inverter powered circuits in your RV. Run the hot output of the inverter to the other fuse input and then the output of that fuse to all circuits that the inverter is covering.
HERE IS THE TRICKY PART ! Do NOT connect the neutral leads from the inverter inside the box to the neutral bar ! The neutral from the inverter covered circuits should connect to the neutral of that circuit. The neutral from the shore power cord should only connect to the non-inverter covered circuit and to the inverter input.
ALL grounds can be bonded inside the box to the neutral. The first outlet on both circuits should be a GFCI.
THEORY OF OPERATION
When on shore power, all power passes through the first fuse before going to both the inverter and the non-inverter covered circuit. This would likely be a 30A fuse. The transfer switch passes current from its input to its output and then to the second fuse which would likely be a 15A fuse.
When NOT on shore power, everything on the non-inverter covered circuit is dead
(including the battery charger). Everything on inverter covered circuit is powered through the second fuse. Bonding is done inside the inverter/charger/transfer switch.
WARNING ! Proceed at your own risk ! I doubt a licensed electrician would install this !!