Hey eurocruising! I'll be on this sailing with my DD (20)
We love Disney cruises - we're platinum on Disney and have been on all of the current ships.
My biggest tip for Disney: You can't do it all - don't try. I'm sure the kids will love the kids clubs - they are truly spectacular!
There are so many things that are specific to DCL...
There are no drink packages unless you get the wine package where you buy a certain number of bottles to enjoy throughout your cruise 0r the beer mug where you pay for the mug and then get a 22oz pour for the price of 16oz each time you refill. Otherwise, adult beverages are paid for as you go.
Since your kids are older, I might consider late dining - You'd see the early show and the kids' club does Dine n' Play, where the dining room expedites the kids meals and the the kids' club counselors come to get the kids during service so that the adults can linger and enjoy the rest of their meal.
The kids club usually will do a Pajama Party one night. And the See Ya Real Soon character gathering on the last night is not to be missed.
Since it's your first Disney cruise, excursions and onboard activities can be booked at 75 days. I would take the time in between to explore the activities you might be interested in, such as Palo - adult dining, Bibbidi Bobbidi Boutique/Pirate League, Princess Gathering, Frozen Meet and Greet, etc.
Feel free to ask any questions you have.