horton333 wrote:
The tow vehicle should be able to provide enough 12 volt to the inverter while traveling down the road, so if you are 'always plugged in' at night there is no need for more battery. ..
That is an assumption which may or may not be true.
Need to know the wattage requirements of the fridge before a good answer can be given.
AND need to know for sure that the tow vehicle really DOES charge the house batteries when moving.
If the fridge were to use the ENTIRE capacity of a 15 amp, 120 volt circuit, that would be about 1800 watts. More likely that it uses half of that or less.......in which case a 1000 watt (continuous) inverter should be plenty.
But don't guess. Find out the power requirements for sure.