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You can - but Florence is quite a lot of walking and in Pisa you park almost a mile from the 'Magic Square'. There's not much to see in Pisa apart from the obvious, but we were exhausted by the time we got there and still faced almost a mile walk back to the coach. One could argue the walking was worth it, but it left us very tired for the next day, which was Rome. You might find children a bit fed-up with trekking around after Florence and Pisa.
It's a few years since we did this tour, but i recall we visited florence first, the coach took us up to a viewing area, quite high, looking down on the city, which was lovely, we then had some time on foot down in florence which is beautiful. it was schoolhols so lots of queues, its also very hot. en route back to the ship we had a couple of hours in pisa, which was sufficient as apart from the tower there is nothing else to see. we were told to stick together as pickpockets were rife, it's not the nicest of areas, especially after forence.
We enjoyed our visit to Pisa, it is not just the tower which itself is impressive but other buildings; market stalls selling everything under the sun and people everywhere having their pictures taken with arms out stretched to make it look as though they are pushing the tower into place. I vaguely remeber the area I think is known as the garden of peace, certainly we saw no problems with pick pockets.
A rock and a hard place! Rather than have a stroppy 11 year old I would choose Pisa, lets face it you need more than a day at the best of times to enjoy Florence and to cut it down to half that would be wicked. My advice would be to farm your 11 year old out one long weekend and go and revel in the delights of Florence at your leisure. .... Ida.
In short the answer is YES as long as you do it by train.
Try this: Livorno 07:30am to Florence, arrive 09:03. Florence to Pisa 13:16, arrive 14:45. Pisa to Livorno 17:00, arrive 17:14. there are plenty of trains in both directions and if you leave the Pisa visit to last, then as you can see it's only a 15 minute journey. If your ship is due to leave Livorno earlier than 18:00 (unlikely) then you can catch either the 16:02 or 16:34 from Pisa.