Same here with that type cooler. 40 degrees cooler than outside temp can be iffy. If you are in 100 plus degrees all the while then a proposed 60 degree internal temp might be okay for water and sodas, but not sure I'd be trusting it with milk, lunch meat or other spoilables. Parents had one they used in their trunk on trips. Needless to say they were not impressed and are using a good cooler and block ice now.
For the money I'm on the cooler program too. Have two sizes. A smaller really nice (and cheap) Coleman Extreme from REI
that has thick walls all around. We use old water bottles refilled and frozen to keep things cool. Sometimes in combo with loose ice depending. Pre chill the night before and then keep the opens to a minimum.
For longer trips we use a larger Engle cooler. That thing is amazing at keeping things cold/frozen. Got it off of eBay
and saved a bit. Wanted something we could take out and not have to power that would keep things good for days.
Power inverter wise advise above is what to follow. Add up all the draw ratings and make sure your inverter has more than that available. Keep in mind how it is installed as could potentially be a draw on the system if powered while the vehicle is off and you have things plugged in. No fun having a dead battery to deal with.