How about going to NOLA and then do a 5-day cruise from there?
We have camped in Gulf Shores, AL several times, then stored the RV there, driven to NOLA and gotten on a ship bound for Mexico, then back to Nola, get RV out of storage, set it back up, camped for another 4-5 days, then headed back north.
Our kids, who are 7 and 10 LOVE to cruise. Before my kids were born, we used to take our niece and nephew with us and they loved the teen program. They can participate as much or as little as they want, but the program is well thought-out for 13-17 year olds. They have their own dance parties, which is usually the girls dancing and the boys sitting around watching, they have game rooms, and other things specific for that age. Then, there's always the pool, basketball courts, water slides, ping pong, just people watching and that kind of thing.
We always let them do whatever they were inclined to do during the day, but it was mandatory that we eat dinner together in the dining room.
You can get rooms that sleep 5 or you can book into adjoining rooms or to give everyone a break, book a balcony room for Mom and Dad and an inside room across the hallway for teens. (That assumes a certain level of trust).
Once you get to Mexico, you can book an excursion that is fun at one port and another that is educational at another.
Just my suggestions! That is a tough age and the more you can do with them and keep them talking and interacting with you, the better things will be all around.