My sense that either Princess or Royal Caribbean would be the best lines for teenage children.
I would not expect to see significant discounts on cruises over the holiday periods to which your children's school schedule obvoiusly constrains you. Nonetheless, there are a couple possibilities for cutting costs. In the Caribbean, the prices for third and fourth berths are pretty cheap -- as low as $199 in an inside cabin on Princess, for example. If you and your husband want a separate room, it might be less expensive to book a minisuite with a sleeper sofa in the sitting area than to book separate staterooms.
Donna raised a very good point about air fare. You probably could knock about $500 per person -- $2000 total -- off the total cost by taking either an "Eastern Caribbean" cruise or a "Western Caribbean" cruise rather than a cruise to the "Southern Caribbean" and thus departing from Fort Lauderdale rather than San Juan. Also, most teens probably will think that the extra day or two at sea is pretty neat, as it gives them that much more time with their peers in the teen program rather than spending another boring day ashore with mom and dad. Additionally, they will enjoy the beach bash at either cruise line's private island in the Bahamas.