I've used dry ice to keep ice cream in a cooler before, and if you don't know what you're doing it will turn rock hard. I didn't know what I was doing.
If I were to do it again, I'd put the ice cream on the bottom of the cooler then some insulation above the ice cream like a thick piece of styrofoam or cardboard, wads of newspaper, and more cardboard (sort of a cardboard newspaper sandwich), then the dry ice on top of the insulation. You won't need much dry ice, just about 4-5 pounds.
Of course, I haven't actually tried it
this way yet, so I don't know how well it would work. But last time I had 8 lbs of dry ice on each side of the ice cream and WOW, solid ice cream.