Hi Francesca,
Not long now until your trip - you must be so excited!
The private cabana areas which you are referring to are called Polar Patios at Disney's Blizzard Beach and Beachcomber Shacks at Disney's Typhoon Lagoon.
They are private retreats with chairs and umbrella shade where you can enjoy a stocked cooler with ice and bottled water, all-day drink mugs, towel service for 6 and your own private locker. Each patio also comes with a personal attendant and waiter service to make sure your every need is met.
I believe that they are priced at around $250 + tax ($150 + tax during non-peak season) and are available to reserve in advance or if available, these spaces may be rented through a walk-up request. The spaces are popular, especially during hot days or peak travel season and are generally spoken for within the first hour of a water park’s operation.
To make a reservation and for current pricing information, please call 001 407 939 7529.
In my opinion, I wouldn't say that it is necessary as there are plenty of places at each of the water parks with regular sun loungers and umbrella shade where your parents could set up camp for the day to read and relax. It might however be a nice treat for you all to experience if your budget permits.
Wishing you all a magical holiday!