The entire world of entertainment, media distribution, and broadcast is switching to digital High Definition at this time. This is happening so everyone around the world will be on basically the same television system with all the same capabilities (unlike the way it is now). The way we can currently share videos, photos, and other media with each other on the internet regardless of what kind of video equipment and computer systems each person has is what the television and home entertainment world is trying to achieve. It will take up to a decade in some areas, but it WILL happen.
When in doubt, ALWAYS record in high definition whenever you can. You said it yourself: This is sort of a once-in-[a]-lifetime opportunity. Film in HD, a format that your grandchildren will be able to use and watch later without the videos looking like your grandmother filmed them when she was a child.
That being said....
If you are going to use this camera for video at Disneyland, you need to invest in some SDHC memory cards http://www.amazon.com/gp/product/B0010LPBRK?ie=UTF8&tag=supportyourlo-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=B0010LPBRK.
If not, you will need to bring your laptop to empty your camera memory from time to time. In between memory dumps, Kodak claims you will be able to record up to 30 minutes of 1280x720 HD video - depending on how many photos you also take. http://www.kodak.com/eknec/PageQuerier.jhtml?pq-path=12456&pq-locale=en_US
You might have to make an investment, but if you have a handful of memory cards, you will be able to stay out longer with the family and not miss anything. You can reuse these memory cards in other HD camcorders too - if you decide to purchase one instead of spending all the money on the memory cards.