I am trying to wrap my head around how I can set this up.

Have a car fridge/cooler currently running from car 12v source (Not constant, source is off when car stops so doesn't drain the battery). I also have a second 12v power source running from second battery, with the intent for it to take over automatically when the car turns off. The 2nd source doesn't charge, I charge it manually in the house, it's just to keep the cooler going during the day.

So if car is on, cooler is powered from car only, saving the 2nd battery. If car is off, cooler is powered from 2nd battery. If car turns back on, power returns to the car 12v source and stops using the 2nd battery.

If it matters, the battery is an 18v power tool battery with a 12v converter.
I also note there seems to be an interruption to the car 12v power when starting the car and turning the key, would that cause an issue? would I need to have some sort of delay also? ie only swap back to car power after it's been on for 30seconds?

 

A couple of options, one you can use a diode ,
Or you can use the car relay as a changeover switch like this...