I think you are confusing the Disney Dining Experience, a discount program for Florida residents and now annual passholders and the dining option that can be added to packages.
With DDE you pay an annual fee ($75 or $50 for AP holders) and get a card that gets you 20% off at selected restaurants (mostly sit-down restaurants and some counter service at resorts and AK where there are no sit-down available). It is good for all meals and includes food and beverages, including alcohol.
With the dining option, you must purchase a package (room and tickets). Everyone in your party must have the same tickets, although they can be for any number of days. You must add the dining option for the entire stay. The cost is $35/night for adults and $10/night for children 9 and under. Children must order off the children menu. You get one sit-down meal (appetizer, entree and non-alcoholic drink, includes gratuity), one counter service meal (entree and non-alcoholic drink) and one snack (popcorn, ice cream, drink). Some restaurants (Signature) cost two sit-down meals as do the dinner shows. They are still changing which restaurants are Signature - just added Le Cellier and Brown Derby.
I definitely agree with the 2 days at park, one day off plan. We did that our last trip and it really helps. We did a water park on our first "off" day and DisneyQuest on the other (sleeping in both days). However we were there in March. The weather is unpredictable in December, so you may or may not want to go to a water park. Swimming at your resort may be an option instead - no additional cost, but can still be lots of fun. Thats what we did when we went in January since we couldn't count on the weather to plan on a water park.
If this is your first trip, I would definitely recommend 5 days in the parks. If you are going between Christmas and New Years, realize this is THE busiest week of the year. It will be crowded. You will want to get to the parks before opening time so that you can get in and get the popular rides done before the crowds get too bad. You will then probably want to go back to your resort for the afternoon and swim/rest and go back for the evening. Because of the crowds, you may want to purchase a 7 day ticket since the price difference between 5 days and 7 days is minimal. That way you can go to the parks for only part of the day on your "off" days. Also you need to plan on doing at least two of the pluses (water park, DQ, Pleasure Island) before it makes sense to add the plus option.
I'm torn myself on the hopping option. We have used it, but not in a major way. On our last trip, we had 4 day hoppers. We did hop to MK in the evening after AK and at the end of our MGM day hopped over the Epcot to ride MS and TT one last time. But it wasn't part of our plan, just spear of the moment thing because we could. With you going during the busy time, it might be good to have if you choose a busy park and want to try another. If you plan on using morning Extra Magic Hours, I would recommend it as the EMH parks get more crowded and it would be nice to hop to another park for the afternoon/night. Since my family has trouble making it before the normal start time, I avoid the EMH parks.
If your 10 and 12 year old like thrill rides, they will love Islands of Adventure at Universal. If not, either go with Universal Studios or skip it for now. However, when we have gone the last two trips, we stayed at a Universal hotel and got their Front of the Line Access. This was great - you show your room key and get in the Express Pass line (like Disney's FastPass) - every ride, any time. With this, crowds don't matter. If you are going between Christmas and New Years, you might want to look into staying at Universal for a couple of nights either at the beginning or end of your trip.
To get to Universal, you can either use Mears shuttle, reserve a town car, use a taxi or rent a car. You can rent cars on-site for a day or two if you want.
Hope this helps some.
