Hi,
You could buy an inverter charger with power assist, such as the Victron Multi-plus 3000. Other makes available. They can do something called "power assist", so whatever your shore power (within reason) they can temporarily make up the missing current needed by taking battery power for the limited time the water is being heated or motor is starting up, then return to shore only and whatever is left goes back to charging the batteries.
I use this facility as do many other boaters to boost poor supplies or even small generators to run washing machines. As for full disclosure, be aware I also supply and install these. I've seen this work flawlessly on a 6A supply, but you do need good batteries, a decent sized battery bank and the shoreline to be stable (i'e, does't trip out because you turned something else on (on the 230v side) or you shoreline is actually shared with the next boat).
If you have a decent (130A+) sized alternator, then it may be possible to run solely from your engine via a large inverter and not via the shoreline, but that's another discussion. Also consider a midi washing machine (3/4 size).
ITA