My advice to you is to sign the 13 year old up in the kids camp group for his age. And at his age he can come and go as he wants without you having to sign him in and out of camp. They will have gatherings and have semi-supervised activities he can enjoy without feeling he is being "watched" all the time. That gives him the socialization and gives you free time. The 17 year old will most likely be hanging with a different crowd anyway.
You may find that you can let go more easily when you know the 13 year old is with a group and not alone. You can use a system of notes in the cabin along with the daily activity news paper to plan and track where he is at a given time. Its fairly easy to find them if you know that the 13 year olds are "on Lido deck aft at the ice cream Sunday making party" or whatever
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013