Based on your signature I calculated you will be on the 9/6 Eastern on the Fantasy. That is a great Itinerary. It has 3 sea-days which give you lots of time to enjoy the ship and it has calls at St. Maarten, St. Thomas and
Castaway Cay.
I will be a first time cruiser in 6 weeks and have read a lot of threads on these boards and the most important advice I found is : RELAX
You will be cruising for fun and enjoyment, not for a stressy feeling that you have to do it all. You won't be able to. Just accept that and you will feel a lot better
Check your kids into the clubs. From what I read all kids love the clubs and don't want to leave there when it's time to go. Don't feel bad about this, that's what the clubs are for. Decide of you want to grant your 13 year old the privilege of checking himself out of the club or not, in which case he must be picked up by you.
You didn't write if you partner/husband/father of your kids will join in the cruise. If so you might consider an adults evening: check the kids in their club and head to Palo for some adults together time. With the wave-phones you will be informed by the councilors if anything is less then perfect for your kids. Palo should be reserved asap as they do sell out.
Also decide if you wish to do the main or second seating with dining. Main dining is early, so the kids will join the entire meal. Second seating offers the kids to be taken to the clubs half way through, giving the parental units time to enjoy late diner. You can do this any night you choose, but are free to choose not to use this service and have your kids stay with you.
Be prepared that the ship will be overwhelming and fun by itself. Enjoy this during the sea days. The pools, slides, view over the ocean and just some time to do nothing and just relax with the family. If you have a Veranda or a porthole room take some private time to enjoy the calming view of the ocean. If not, take some time to relax on deck with ocean view.
On port adventures: just check the list of
DCL offered adventures and see if there is something you and your family will like and if it fits in your budget. I think for first timers it is relaxing to book these with Disney. When you are comfortable to do this on you own, you should try that on your next cruise.
The only thing you shouldn't do is: stress
as this will spoil the entire vacation.
Relax and you will have a great time, no matter what happens and what doesn't happen.
Happy sailing!