Ok, your 12 year old will be in the Lab, so you will have a pager. Any of the kids can go to the lab and ask to have you paged any time.
My DD turned 13 on our last cruise, and LOVED the program in The Stack. No way she would have wanted to be back in the lab. The kids in the Stack are divided into a 13-15 and a 16-17 age group, the same way the Lab kids are divided 8-9s and 10-12. You will probably be allowed to move your 13 year old down, but you are only allowed to move him once, and it is then a permanent thing. I'd suggest that you start him in his age appropriate program, and then move him down if that doesn't work for you/him. I just can't see a 13 being happy in the 10-12 program. DD at 12 thought it was "lame." (We have done the Magic 10 times, so she's been in all kid locations and most age groups.
The Wild Side is a teens only excursion on Castaway Cay. It is a 4 hour thing and includes snorkeling, kayak, biking, and fun time all with the teen counsellors.
THe kids in the club and lab are sometimes in other locations--these are noted on the kid navigator which you will get when you register the kids. They go to Topsiders for meals, they go to Animator's Palate for some craft activities, etc. Also, the club kids have some time in the lab and the lab kids "invade" The Stack before it opens for the teens (the teen program starts at noon!)
We do the deal where DD has to be either in THe Stack, in the cabin, or leave me a note in the cabin telling me where she is. 12 is plenty old enough to have the run of the ship on their own...especially with brothers. I'm sort of hyper and super conservative (according to standards of other parents around here), and I feel very comfortable with DD being free on the ship. Of course, after 10 cruises, she feels like she should be a crew member!