Very sorry to hear of your troubles when you arrived in Florence, particularly with the missed train connection - never any fun finding the best next one to get to where you want!
As you might have ready in my earlier posts on this particular thread, when you call a taxi here in Florence they give you the name of the taxi that you're to expect. It generally is the name of a city and a number - such as Berlino 125 or Roma 456 or something of that sort. They say it in such a matter-of-fact voice that you might miss it if not prepared for it, since they don't tell you "here is the name of your cab" before saying it. It is just likely that with so many cabs arriving for all the passengers, someone else took yours!
Definitely your daughter needs to know how to call one during her time here, and also know that after 9pm, if she's alone, she should catch a cab and get a small discount. She needs to ask for the 10% discount off the rate given for women traveling alone at night once she arrives at destination, they won't give it automatically.
So when you call a cab, just indicate the address where you're at, be prepared for their answer:
the approximate time it will take for the taxi to come pick you up and the name of the cab - or maybe in the other order, don't recall right now!
You can also call for a taxi with a text (SMS) message.
For the
055-4242 So.Co.Ta. taxi company, the number is:
334-6622550
while for the
055-4390 taxi company the number is:
333.8077555 (this second one also offers calls with Skype at "taxi.firenze")
In the message, send the address where you need to be picked up (street and number).
If it's a restaurant, hotel, cinema or something like that, indicate the name of the place and add your last name to the message.
You'll get an SMS confirming your taxi with the name of the cab and the estimated time for it to arrive at your address.
In this way, you can also reserve a taxi for tomorrow or another date... for example:
"via aretina, 12 - per le 6.15 del 02 novembre - Rossi" (the address, time and date for pick up, last name).
Oh.... if you're heading OUT of Florence, in the SMS indicate that your destination is out of Florence so they'll send the appropriate taxi.... otherwise is is always assumed your destination is Florence.
Hope this doesn't happen to you or your daughter again!