What we use has changed over the years. We started going when my son was 10 months old so back then I had a backpack that could double as a diaper bag. The past few trips it's been mostly drawstring backpacks and as the children have gotten older they carry their own. They're light so they're not hot on their backs and they're easy to search at park entry. And they fit under a poncho without issue. We're down to just carrying poncho, cooling towels, handheld fans, meds, money, female items when necessary, a snack and maybe a light jacket for table service meals and our phones with a portable charger.
Last year we made a change. I switched to a backpack cooler and packed it with drinks and ice in Ziploc bags. We put my poncho and other items in my daughter's bag. There's a front pocket on the cooler for my phone. I'd hit the ice machine before we left and fill 5 or so snack-sized Ziploc bags with ice. Since we can't freeze drinks in the resort room fridges, it was great. I wish I'd switched to it sooner. I had carried drinks like that before; but not in a cooler bag so the ice didn't last long. The drinks were from our in room grocery order so everyone had exactly what they wanted to drink at any time no matter where we were and it was nice and cold. It's been so hot this summer, my son started using the bag to bring Gatorade bottles to soccer camp because it stayed cold as opposed to me filling a 64 ounce jug in the morning. So it's his now. I ordered a another one for this and future trips.
Wishful thinking 
