Your kids are an awesome age for the cruise b/c they can all be in the same club together! Of course, they may not want to be, lol, but they can.
There are two kids clubs for ages 3-12... one is the Oceaneer Club and the other is the Oceaneer Lab. Exactly what's in the them varies a little by ship. Your older child can also go to the Edge (for ages 11-14).
You can pre-register your kids online or at the terminal. That saves you a little time, but you can also just do it onboard whenever you go there the first time. Either way, before you take your kid into the Club/Lab for the first time, you will get them something that looks like a MagicBand (
http://disneycruiselineblog.com/tag/mickey-band/). You pay $12.95 only if you don't return them (some people keep them as souvenirs or I heard they also work w/ the Disney Infinity game?) It has a chip in it that's used for checking the kids in/out.
With the Club/Lab, you can choose whether to give the two older kids checkin/checkout privileges. With the Edge, you don't have a choice (all kids who go there can come/go as they please- and as far as I know there isn't even a scan in/out system there). Edge programming includes things that take place outside that space itself, such as scavenger hunts around the ship, etc. How parents handle that (i.e., the amount of freedom given or communication required) varies a lot by child and family but I'd say the best thing is to treat the ship like any other public place (such as the Mall).
The Club/Lab and Edge have Open House hours, during which time anyone can go in/out. But if the Club is having an Open House, then the Lab will have "secured programming" and vice versa. So if your drop kids off in one but then the schedule switches to an Open House then they move the kids in there to the other location (i.e., if you left them in a "secured programming" they'll stay in "secured programming", even if that means moving them from the Club to the Lab). Normally, adults aren't allowed all the way into the Club/Lab (except just to drop off/pick up your kid) but during Open House anyone can go in and look around, or even play in there, which is great if your kid wants to spend time showing you all their favorite games/toys, etc. (And even better for families who for various reasons aren't able to be in there at all or not all together.)
The Club/Lab and Edge also have a variety of totally-optional scheduled events, which your kid can participate in or not. Your daily schedule (the "Navigator"- available in paper copy and on an App that's somewhat new).
If your kid is left there during a mealtime, some basic foods will be offered at the standard mealtimes but no one is made to eat anything (and often kids playing just choose not to eat).
You should keep your Wave Phone on you b/c that's how they'll reach you (the new App they have is awesome but at least when we were there last Aug, the CM's weren't using it w/ guests). If your kid really needs you, he/she can tell the CM and you'll get a call your Wave phone.
If I've gotten some info wrong, I'm sure it'll be corrected. There's a lot more knowledgeable and experienced people on here!