Since you will be going in the summer when lots of the ships will have left the Caribbean, could I suggest Royal Caribbean? I can't remember if it's Voyager or Explorer of the Seas that does the Eastern Caribbean but they are both RCI Eagle class ships, the largest ships afloat at 142,000 tons! There are so many things happening on board that you will be hard pressed to have a single dull moment. If you need your cruise to be a little more laid back, try Celebrity's Century, a total class act.
This summer there are lots more choices in the Caribbean then there has been in the past. At this time of year the children's and teen programs will be fully staffed on most any ship you choose.
Two other great choices (besides the Royal Caribbean mentioned elsewhere) are Celebrity Century and the Grand Princess. premium cruises in leegant and fun surroundings at copmparable prices to the RCCL choices.
If you are budget concious you might consider Carnival as well. Especially the newer ships are very well staffed and nicely decorated. They are the tops in kid's programinmg.