We rent umbrellas every time we go. It makes it easy so that we don't have to worry about finding chairs, our stuff is somewhat protected and it gives us a good meeting place when we are separated. Plus, there is a lot of room in there and the umbrellas are pretty well spread out, so you don't feel like any other party is on top of you. Also, the foot traffic is a lot less, so if your 15 m/o just wants to sit and play in the sand, they can and you can feel relaxed that they won't get tripped over or in someone else's way.
Disney is great, but there are certain convenience upgrades that make it 10x better—this is one of them.