we initially wanted 3 double rooms for 6 people. Supposedly, the travel agent said that the cruise was booked up and we would need to take two triple rooms instead.
Did the agent say there were not 3 cabins available on the whole ship, or in the category you wanted? I'm seeing several double cabins available, but I don't know if they're in the category you want. Some categories are sold out.
As for the third person in the room, some rooms have an "upper" bed that folds out from the wall. Other rooms have a sitting area that includes a sofa and chairs. The sofa is a pull-out double bed, and the sitting room is separated from the main bed area by a curtain.
The pricing is structured such that the first two people in the room pay the double occupancy price, and the third person pays a reduced rate. The double occupancy rate depends on the category, and on Royal Caribbean, the third person rate is the same no matter what category you're in. The room is the same room whether you have 2 or 3 people in it.
What my clients usually do when there are 3 people in the room is take the cabin total and divide it by 3, so that the price is the same for everyone, as it averages out.