We're at about 13kwh per day, but that is bound to increase as the girls get older. Also, the new place has a couple of aircons which would be nice if we could actually use them.
Don't confuse peak load with average load.
A 2 kW geyser element takes about 2 hours to heat up my geyser. It uses 4 kWh to do so.
A 4 kW geyser element takes about 1 hour to heat up my geyser. It uses 4 kWh to do so.
If you use those 13 kWh all in one hour, you'll need a 13 kW inverter. If you manage to live in an ideal world and spread those 13 kWh equally through the day, you will only need a 1.85 kW inverter.
In my setup I have a 4 kW/5 kVA Victron inverter. Most of my load is less than 3 kW, so most of it is supplied by the inverter. Sometimes, though, I'll have the kettle and geyser on at the same time, and then my load will be a bit over 4 kW. In those times the inverter pulls 4 kW from the panels/battery, and the missing bit from Eskom.