a pass through inverter would have solved
both of those issues...
have you fused the coil lines from the shore power plug
I would probably have left the shore straight to the ac panel to the main. have it feed the charger, HWT, other non inverter loads direct from their breakers. then have the relay control between shore and an inverter only section on the panel that would be used on inverter. so split the ac panel buss.
the invertor should not be able to power the whole boat. the panel should be split into inverter and non inverter loads. it's easy with a passthrough inverter. but could be done with your inverter and relay as above.
if the charger is the only thing not used on the inverter then it's probably ok. but will confuse anyone coming to work on it in the future as it's totally non standard
(most boats have a HWT, range, and other stuff never used off an inverter)