We have a Domestic washing machine in our motorhome.
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Although compact it will take up to 3.5kG load. It will run off our two 110ah leisure batteries via the inverter and solar panels BUT ONLY ON A COLD WASH
. Otherwise it can be run as normal when on EHU. The water is fed from our main tank just like our taps and drains into the on-board grey waste tank.
The most important thing when considering fitting a domestic machine to run on an inverter, is for it to have temperature control option or at least a cold wash option. This allows you to do an everyday wash without using the heater. The heater is main consumer of power during the wash, ranging from 1500-3200 watts.
If you have the room then you can fit a standard 5kG+ washing machine. Though bear in mind you will have factor the extra weight of this on your payload/axles.
Hope this helps?