you need to split up the ac panel. you don't want the Hot water on the inverter either.
so you'd have shore power - main double pole breaker - inverter breaker and HWT breaker input side - inverter breaker output side- inverter - AC plug
put the HWT and inverter breakers side by side you can cut the bus bar between those 2 breakers and the outlet breakers
you also need to split the neutrals up. so on the white wire youd have
shore power - double pole main. shore N bus with shore input, HWT, inverter input. then inverter output to inverter N bus with outlet N's
the inverter in and out wire should probably be 10/3 and make the inverter breaker 30a. (your existing charger wire is probably only 14/3)
are you on 30a 120vac shore?
make you have correct size battery cable (probably 2/0) with an inverter switch and class T fuse (probably 250a). inverter should be within ~5' from batteries
. Most people aren't going to have the tools to make 2/0 cables