The policy is that they must be within 30 days of the next birthday to move up to the next group. What is NOT allowed is just what you suggest--moving back and forth between groups. Your son will need to be either in the 10-12 in the Lab OR with the 13-15 in THe Stack. Each child is allowed only one move during the trip.
I would suggest 2 things. First, talk to the counsellors. Secondly, start the 12 year old off in the Lab group. Then, if he wants to move up to the Stack, the counsellors will have had a chance to assess his maturity, and this could be his one move.
There are many times and places that the boys can be together outside of the programming. There are "family" activities scheduled throughout the cruise. THese range from building a race car out of vegetables, "toad race" (the toads are not alive!), pictionary, etc. The list goes on. In addition, there are scheduled family times in the Lab where kids of any age can use the facilities there with the parents. In addition, there are deck parties, sports activities, the arcade, etc....and that doesn't even begin to start with the entertainment stuff.
Do talk with the counsellors because the occasionally slide the rules a little to keep families together.
There is registration for the Stack, but the teens come and go as they please after they are registered as participating. They don't have sign in or out, and there is no parental notification system for them.(no beepers, etc.)