How fun! My husband and I have one daughter, who is now 6, and as a family have done quite a bit of travel. If I had to recommend one cruise line, which you wanted to be geared mostly toward your children, I would have to recommend the Disney Wonder. Not only are the cabins one of the largest in the industry, the food great, but the kids' programs are terrific. They are now doing 7 night cruises as well, and they hit their own island, which is pristine. When we went 18 months ago, we did the 3day land/4night cruise package. Our daughter was 5 at the time, and thoroughly enjoyed it. More so then any other place we've taken her, although we're taking the Radiance to Hawaii in Oct., we'll see what her then 7 yr old perspective will be.
As adults, you will also be impressed with the marble, art, service, and great entertainment the ship has to offer. I would be hesitant to go on a Carnival cruise with a young child, as I've always found a "partying", more crazy atmosphere on board, when travelling on Carnival.
Either way, cruising is a fantastic way to enjoy a family vacation, we always do one cruise, and one land vacation each year, and the cruise is always the favorite for our daughter!!