I suspect it happens on the metros (subways) more than actual trains that go city-to-city. The biggest challenge is getting ON the metro with the crowds pushing around you, especially during rush hour. Our group got separated in Rome when 2 of us made it on and 2 didn't.
The metros run on the same lines however, so we just got off at the agreed-upon stop we were traveling to and waited until the rest of our party arrived.
Getting off the metros is easier--just make your way to the doors well in advance of your stop. Often there will be a crowd of people getting off that will just sort of 'carry' your along. If not, push your way through politely, but firmly (for Rome at least!).
For your daughter, as other the poster suggested, make sure she has some money and/or a travel pass, and the name/address of where you are staying. If everything goes completely wrong, she can get a taxi back 'home'. Also, if the metro looks crowded and you're concerned about not making it on, just hang back and wait for the next one.