unsurecruiser- The FIRST thing you need to do is to take a deep cleansing breath and relax. You are going to drive yourself insane worrying about this cruise. Its supposed to be a relaxing vacation.
You are not the first person to cruise with a 2 year old. The cruise lines are set up to be more than able to handle your needs. They do have cribs available and there will be enough room for all of you in the cabin (even without the upgrade which to be honest, only adds on the balcony to the cabin size unless you got a junior suite balcony cabin).
The lack of a tub has not seemed to be a big issue for other families with small children. As Islandcruz stated, the shower head is on a hose and you can take it down to rinse/shower off a little one. The childrens activity personnel are wonderful too... don't worry about it so much, they have it down to a pretty good system. Just be sure to attend the kids orientation party/meeting and all will be explained to you.
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