Playmate coolers-anything better to keep meat frozen?

We seem to be taking more road trips to Amish butchers in Ohio, Illinois and Indiana and bring back steaks, ground meats, pork, sausages and other pershible meat and cheese products. We also drive to Lousiana twice a year over 4 days and stock up on gumbos, smoked meats etc. We have a few small/medium sized playmate coolers and pack them with ice-reloading ice every 12 hours. The already frozen meats stay frozen (or soften slightly) but there is plenty of ice and water which makes the process more cumbersome-(I use Ziplock bags to prevent leakage into the meats). Is dry ice better? Will it burn holes through these plastic coolers? Is it better to get the cheapo styrofoam coolers? Is there a brand or type of cooler that you all use when you go on shopping trips? is multiple smaller coolers better than one big cooler in terms of keping things cooler for longer periods? If dry ice is the way to go-is it hard to find if not sold on site and any adverse effects such as freezer burn? Any recs would be most appreciated.

I have one of these Coleman Thermoelectric coolers that I use for road trips. It plugs into your cigarette lighter and/or AC. You cn find them online or, like me, you can buy one at Cabela's

I could have sworn I replied to this earlier. Dry ice is the neatest solution because there's no melted runoff or residue and it can easily keep for a couple of days (just don't keep peeking inside). I used it for week-long camping trips many years ago. Just wrap the blocks in newspaper and fill up as much of the excess volume in the cooler with crumpled newspaper. And leave the drain open so you don't build up pressure from the expanding CO2 (not a real hazard, just good practice). As for where to buy, many ice houses will carry it and if you're in a strange town, ask the butcher (or ice cream shop) - they'll direct you to the right place.

One more thing: don't forget that "cold air sinks" so the blocks of dry ice should go on top of the frozen food in the cooler.