Just got back from a week and a bit on Belize Aggressor and Ambergris Caye. There were lots of folks with children and teens vacationing on AC and depending on the teen and where you stayed, they probably wouldn't get bored. Tons and tons of dive operators to choose from.
I really like Ambergris Caye and will definitely go back. Highly recommend the mixed jerk platter at Jambal's Jerk Pit.
Belize City is not a place to go wandering you know. We flew from BC airport to AC on local shuttles. Ensure that you coordinate safe transfer plans with your final arrangements, ASAP.
'safe transfer plans'? That sounds a little extreme. You're very safe transferring to Tropic Air (same international terminal as American Airlines or a taxi ride to the municipal air strip) or taking a cab to the water taxi terminal (I don't think you can even make a reservation for that).
We flew Tropic Air out of the International terminal to AC, and then back to the municipal strip. We had reservations, but many folks just walked up, bought a ticket and got on a plane. If the Tropic plane is full, you can wait an hour, or try Mayan Air. Even though we had reservations on a later plane, they just jammed us on the next flight. Tropic Air rocks.
Belize City is pretty safe during the day if you stick to the open areas and the main business street downtown. I wouldn't wander down there at night. It's just not interesting at all, and parts of downtown stink. There are also a lot of grifters and beggars that hang out by the water taxi terminal, the park by the bank and in front of Broadies. By day they are harmless and there are lots of cops and security guards around.