There are heaps of combinations you can use for this little problem, on a limited budget, depending on your camping requirements.
My sollution to this evergreen problem, grab a 12v portable fridge from 40 to 50 ltrs in capacity, there are various makes on the market, shop around and haggle....
Then buy a quality built esky(everkool, Coleman etc), again about 50ltrs in capacity.
You keep the foodstuffs, milk, butter, salads etc in the fridge on -2c or 0c.
Then in the esky, keep the ice, frozen water, beer etc.
Why, 90% of the time, the kids and you are in the fridge wanting drinks, plus it saves energy for the fridge to do its stuff because you are not in and out of the fridge all the time, think of the kids into the fridge at home...
My set up is at the moment, a 12volt Bushman, with a collar and high dome lid, expandable from 35lts to 50ltrs for the foodstuffs etc, a Coleman heavy duty esky, that keeps solid ice blocks (not party ice) for 4 days.. all up about $1200.00.
The Bushman cost about $990.00, with the extras thrown in, thermal cover, 240v power adapter, high lid dome, collar and extra baskets (got it at the Qld Caravan and Camping show as a special) and the heavy duty Coleman esky, $150.00.
It does the job for me and my clan perfectly.