here are my thoughts... sorry folks.
Liveaboard = No freakin' way I would put 2 teenagers onboard a boat for even 1 week with a dozen adults. That would be insane. At sea, no place to get away but their cabin. You would have a mutiny.
I would go with a land-based trip. Do your diving daily and still give the teens a little space to be teens. There are dozens of places to go.
Even though you have a large budget, I would not spend that.
You could go to Cozumel, do a nice All-inclusive (yes, I would do that as food is unlimited and teens eat constantly!). They have pools and a beach.
That way you could do a week there, diving every day, then maybe a few days over on the mainland doing Mayan ruins like Chichen Itza, some cenotes, etc. Maybe even do a day of diving in the cenotes. You could do all that for under $20k for 4 people.
Just my 2 cents.