We got a couple EchoSmile (knockoff Yeti) coolers a year ago and we still love them.
If we're just going out for a quick day or evening, then we just fill them with ice and go. But if it's going to be multi-day and we need the ice to last, then I fill the cooler with ice first to cool it down to temp, dump that ice, and then finally fill it with food/drinks and fresh ice. This works pretty well.
I also use the bigger cooler to let my meats "rest" when I've cooked something big on the smoker. The cooler will keep a brisket or pork butt warm for hours if you warm up the cooler first. I have some ratty old towels that I use for this and I put them in the dryer to heat them up and then put the hot towels in the cooler to get it warm in there. Then when I'm ready to take the meat off the grill, I reheat the towels and wrap the meat in foil pans and warm towels to let it rest before mealtime.
If you end up keeping your soft cooler, try pre-cooling it before your trip and see if that doesn't make your ice last another day or so. And make sure the food & drinks have been chilled first too, otherwise a warm cooler and warm foodstuff will melt that ice almost instantly.