Leave the laptop at home. The kids will be so busy that they will forget about email. At $25 for 30 minutes, if they are that hard up for email, make them pay for it themselves. At the slow data rates you may get at sea, it may take 30 minutes just to download the spam.
The other option is to wait until you get to port. I'm sure Cozmel and Grand Cayman have internet cafe that may have cheaper rates than the ship.
Or, introduce the kiddos to that long forgotten form of communication called "the postcard". It will make their heads spin to think anyone actually survived in the olden days.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013