So twelve 30-minute discs for 14 days works out to slightly less than 1 disc per day. How much do you shoot in a typical day?
On my last trip with a video camera, we shot 4 hours of video on a nine day trip with 6 days at the parks. Excluding the two travel days (during which we shot no video), that worked out to just over 30 minutes per day.
If all you plan to shoot are family activities, you'll probably be OK. If you want to record some of the shows, you'll probably run short. After all, a typical parade or show is 15-20 minutes by itself. That doesn't leave you much extra time if you're shooting less than 30 minutes a day.
No one can tell you what the correct number is because no one knows how much you'll shoot. For me, I would probably bring 1 hour per day worth of recording media. I would probably not use that much, but I'd prefer to have too much instead of too little.