I used child swap two trips ago, not my most recent 2014 trip, but unless they've drastically changed, there's no "designated area". I always wandered, shopped, took a bathroom break, had a snack. Maybe a specific ride or two has special areas, but I can't think of any.
Before I ever used it, i pictured that the whole family entered the line together and the parents just took turns standing with the child at the platform. Maybe obvious to others, but that's not how it works - the waiting parent gets a paper ticket, the first parent waits in line alone, then they switch and the 2nd parent uses their ticket to bypass the line and go (nearly) straight to loading.