As others have said, they can all be together in the club/lab and your 12 year old can also go to Edge. The older two are old enough to be self-check outs (they can all check in by themselves), if you give permission (even if they are Edge age you still have to give permission for this), Edge is come and go as they please and there is no checking in or out. The 12 year old can go between both spaces as much as they like and don't have to chose.
If they want to leave and tell a CM, then a message will be sent to your Wave Phone, there will be two in each stateroom. Yes, kids can communicate with you via the app, but if theres ever an emergency or there are any questions from a CM, then the WP (or room phone) will be the only way they can contact you.
On all the ships now, the club and lab are connected so they can move freely between both as much as they like when they are in secured programming. If you have dropped the kids off and one side goes into Open House, then all children that are checked in will be safe in the side that is in secure programming.
Once in they can do what they like, all organised programmes and activities are (should be) announced and usually all counsellors around will encourage children to join and at least give it a go, but they are also able to use the iPads, wii, crafts, games if they choose to. There are counsellors in every room, at the gates and outside the bathrooms.
If your worried about kids not wanting to go in, check out the OH times, which go on in both spaces up until the drill on the first day. Parents can also come in for a few minutes to get kids in if you really need to when dropping off. As to whether they will like it, you won't know until you get there. As first timers, your kids have probably never been in an environment like it before. Ive had parents say their kids are going to hate it and will want to leave within minutes and they have they end up having to drag them out, and also the opposite way around.
Dinner is served usually around 6 every day but will be on the navigator (apart from embark day) and any kids in care will be offered food, but if they're not going to be there are that time, or you want to be sure they eat and want to know what they eat its best to feed them before hand from room service or the pool deck.
If you are going to Palo (or the spa, or just want some time apart from the kids) you can let the CM know when you check in, they can make a note of it and that way they will refrain from contacting you (unless its an emergency, obviously), and redirect the kids and entertain them.