You should have started them diving when they were 3, too, as I did with my ones. Of course at 3 years it means inside a pool, but after 3 years in the pool, at 6, they could have been started diving in the sea (in warm water, no diving suit, no BCD, minimal depth)...Thank you everyone for the advice and feedback.
Someone mentioned paying a guide $25 per person for a 2 dive boat trip. Another mentioned $110 for group of four for two dives. Is that somewhat standard? There are a few dive masters from my LDS I've become friends with here that we can go with around here, but what is the best way to arrange a guide when we go on trips? Contact a LDS ahead of time, post on SB, etc.
Lastly, to answer a couple of questions / points raised:
1. My wife is not interested in diving with us. She took an intro to scuba course 15 years ago and realized that she has a fear of depths.
2. I understand that taking the AOW course this soon after taking our OW is not ideal. The AOW is on a cruise (Nassau) and this will be the first opportunity to dive somewhere other than a quarry in PA with poor visibility. We all understand that we won't get as much out of the course than if we had more experience, but we are using the course as an opportunity to dive together with good supervision in good conditions.
3. I recognize the "squirrel" tendencies of 12 & 13-year-old boys. My sons follow directions well when we're together doing outdoor activities. I started each of them skiing when they were 3, and the 3 of us have been skiing regularly together since then. So they're used to having a plan and following instructions. But of course they're still 12 & 13.
Starting at 12-13 requires much more attention and control, hence the need for diving guides following them.
The idea of a vacation in warm waters where AOW training is provided is a good idea, for me.
Being part of a class places the students in "learning mode", where they have a goal to reach (the certification) and hence they tend to be more obedient and self-controlled.
Probably having to perform various skills will make the dives less enjoying than purely touristic dives, but safety comes first, so I think it is a very good idea. And possibly you could repeat the same in following years, adding every time some "specialty" such as search & rescue, deco diving, deep diving, free diving (which is probably the most important one), etc...