I am confused as to the problem statement?
Anyway, we freeze small plastic bottles of water and just throw them in a small cooler with drinks on the way out the door. You can drink them when thawed. My wife uses them in a cooler bag when bringing home frozen food from the store. Throw them back in the freezer when back home.
No mess.
For variety, you can also freeze the plastic bottles of green tea and some sports drinks. Not recommended for carbonated stuff.
For reusable, no mess, cold on a road trip, use wide mount plastic jars (peanut butter, mayonnaise, etc.) with frozen water. Refill later with purchased ice.
Does this help, or is this a solution looking for a problem?