Is it possible to travel from florence to cortona and from cortona to sienna and back?
It definitely is possible. But, you can't do it all by train only. For Cortona, you take the train to either Camucia or Terontola where you then take a bus to Cortona. From Cortona to Siena, you most likely take a bus to the Camucia station where you can take the 2-hr train ride to Siena. I believe that there is also a bus run but I can't locate it at the moment. From Siena back to Florence, you can either take the train for the SITA bus. Note that the train station is almost a mile slightly downhill from the town (bus and taxi available0 and the SITA bus terminal is at the City wall.