Yes, you could do it. You will need a 30 amp 120 volt shorepower inlet for the charger-inverter. This would then go to a double pole breaker like this 120V AC Main Circuit Breaker Panels - Blue Sea Systems
and then to the inverter. The inverter AC output can go to any GFI outlets you wish to be 120 volt. These will be totally separate from any other power source.
The DC input to the inverter will need a fuse on the positive input like this ANL Fuses - Blue Sea Systems
and for an inverter of this size 250 amps fuse size and 2/0 wire size.
Thin inverter-charger that meets your 1800 watt -40 amp charge requirements is this one Inverter Charger | Freedom HF Inverter/Charger | Xantrex
Its control panel is designed to be remotely mounted for convenience.
I would keep the Dolphin charger for use in 220 volt countries. It will work fine but will take longer for a given amount of charge.