How does the dining work?

On these disney cruises, how does it work?

Are you rotating around a set of different restaurants? Can you choose to stay at one even if you pay more?

Are there any tables for a family without having to share with others?

You rotate among three restaurants on the ship and your servers remain with you. The only restaurant outside of the rotation is Palo's for which there is a $15 surcharge per person plus a tip which should be 18-20% of what the meal might have cost had you actually had to purchase it. Otherwise you must do the rotation. However, I believe that rotation only pertains to the evening meal, I know it doesn't necessarily pertain to breakfast and I'm not sure about lunch. It depends on how big your family is. We cruised with another couple and we got a table for 4. Other tables sat anywhere from 6 to 10 people.

As uscwest said, the rotation dining applies to dinner only, you are free to take breakfast and lunch wherever you fancy and then obviously you will be able to have a table all to yourselves.
You could also have dinner at Topsider`s every night if you wish, apart from the first and last nights of your cruise, and again you would be seated by yourselves.
That said, whenever I`ve been on a DCL cruise there has normally only been my DW and I, and as such we`ve always been assigned a table with other folks.
I must admit to feeling a bit nervous on the first night, not knowing our dining partners who we will be seeing every night of the cruise, however so far we`ve met some really great folks this way and we`ve kept in touch with many of them since...some of them are even members of this site now! :thumbs_up:

The rotation is only for dinner - you can eat anywhere for breakfast and lunch :p015: We are a family of four and were seated on a table of four, we were quite close to the tables either side of us - we all had the same servers, it worked out great because we were close enough to the other famillies to chat about our days but far enough away to not feel we had to wait for them to order or leave our table.

Your table number stays the same in each restaurant so you are seated next to the same people each night and your servers rotate with you so they get to know your needs and you find on the second night they already know what drinks you like etc.