Hi,
You can also make some blocks of ice before leaving on a trip. Put some in a 2 quart tupperware container, and let it freeze at least 48 hours before leaving. Might even put some in a zip lock baggy (so the blocks of ice will not get freezer burn).
Blocks of ice tend to stay cooler longer. Yes you will need a better insulated cooler too. Also if you are putting in warm soda's to the ice, you will use a lot of ice to cool the items. Say there is 1 gallon of soda, that is 8 pounds, and if brought from 82F to 32F that is 400 Btu's or enough to melt 1/2 pound of ice.
Cooling the same 8 pounds from 39 to 32F is only 56 Btu's or about 1/20 pound of ice. So refrigerating the items before putting it into the cooler will help a lot.
Fred.