I have travelled around Australia twice and go away every second weekend, often with my 3 year old. I have three 1.5 litre water bottles and one 2 litre cordial bottle. All are sealed with the normal plastic screw caps and contain 90% water. They are in the freezer in the shed.
Before I take off I put them all in the bottom of the esky.
Perfect fit.
Then I (read wife) put all the food and beer in. The esky stays cold and dry for a few days and the spare water in the bottles can possibly be used in the unlikely event of a breakdown in the middle of nowhere?
If I'm planning to drink more than 4 beers a night or want super cold beer I buy a small bag of ice and put it on top.
I have a dual cab ute with a liner. I never leave the esky bung in and simply let any excess icey water drip out and away. The ribs in the liner are 10 mm high so the water drains away and no other bags get wet. If I had a wagon or car I would be inclined to attach a hose to the bung and direct it outside, or not buy ice and rely on the bottles, or simply leave the bung in until we reached the destination.
When I get home it takes about 12 seconds to hose the esky down, turn it upsidedown to dry and to put the bottles in the back freezer.
On longer journeys we grab ice during one of the many daily stops or put the bottles in the camp kitchen freezer at the caravan park overnight to re-freeze. And then I am able to offer a jump start to anyone who requires it in the morning

before leaving for another day of discovery.