The category 12s on the fantasy class ships are not so huge that a family of four would be really comfortable. There are two twin beds which will convert to a queen and a sectional sofa with a pull-out double bed. If the kids are older, it will be a tight squeeze. I wouldn't think that a cot would fit too well. There is also the bathroom issue. There is only one bathroom and, as far as I know, the cat 12s are the largest on this class of ship. (Destiny class 12s are really huge and would be more well-suited to more people).
We tend to pend lots of time in our cabin. That's why we chose to book a balcony. It is relaxing for us and we like the extra space. Although we do not have to justify our motives to anyone, we certainly have done our share of the lower, inside cabins over the years.
The category 6 cabins are surprisingly spacious. I like the bathrooms better in the 6 than the 12 -- the tub is too small to use and it is a pain to step over it to take a shower. There is plenty of room in these cabins. I think that you would be very happy with these accommodations. I was very impressed with the size of Carnival's cabins.
I have some photos of the category 12s. If you like I can send them to you.
judy and steve