We cruised last CHristmas on the Magic with a family group of 19 for my mother's 80th birthday. Age ranged from 10 to 80.
Disney cruise was perfect, because there was something for every age, plus plenty to do together.
For dining, we linked our reservations and had 3 tables and the 2 servers just for our group. You would probably have two different serving stations with 30 people. Disney would probably put you next to each other. Each night we sat in different places so we got to talk with different people. No formal rotation, just did it.
For the beach days, we decided ahead which beach we would go to - no organized tours - and each family group headed out by cab when they were ready. The first ones to the beach rented enough chairs and umbre llas for everyone, a few took coolers with drinks, some took those fantastic chocolate chip cookies from room service, etc. the food was not planned - just happened.
Be sure to gather together before boarding, and they will take a photo with all of you. Also on foraml night you can get a nice group photo.
We had matching t-shirts that one brother and his wife made for us with embroidered logos - even had a hidden mickey. It was fun on the first day because we could find each other easily for the sail away, etc.
We generally went to the shows together and many of us would head to the clubs afterwards. A few times we all met on deck 10 before or after dinner just to sit and look at the sunset or stars. Those were the best times.
ou will have a great time - Disney is a great family line with a focus on fun activities.
Here we are boarding the boat:
http://home.columbus.rr.com/parents/fam/teeshirts.jpg
There have been a few other threads in the past month about large groups. There is more information in them from people who have traveled in groups larger than our 19.