Why do you need to change trains at Pisa Rossore?
You can go through Pisa to Florence without changing trains.
These are commuter lines and you probably won't be able to buy your tickets on line ahead of time, but you really don't need to.
Yes, the taxi's are hard to get to take you to the station in Livorno. If you get one willing, be prepared to pay 20 eruo per taxi. (we got eight people in ours so it was only 5 euro for each couple) But, the port runs a free shuttle form the ship to the Central market area. You can catch the #1 bus to the train station from there and the 1R route back(ask the bus driver if they don't tell you how). The taxi is quicker and more direct but you pay a price for that.
Tell the ticket office that you want to go to Florence but want to be able to stop in Pisa.
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