Transportation from Florence airport

Colle VE and Cortona are nowhere near each other. The former is toward Siena and the latter is toward Perugia. Did you mean Volterra instead of Cortona?

We first must find transportation for 2 with luggage to the Palazzo San Lorenso Hotel at 53034 Colle di Val d'Elsa and after a week we will travel to stay in Cortona for 2 days. We need transportation for 3 with luggage to Cortona.
THANKS for the help

I hope that your flight is arriving early to give you some flexibility with bus schedules. Buses run every half hour (6:00 - 23:30) from Florence Airport to Florence's main train and bus stations. It sounds like your bus destination is Volterra, not Cortona, on this day. Connect at the bus station to other service operated by SITA a.k.a. FS Bus Italia to Colle, then a connection on CPT bus #770; you can only do this 4x/day (or once on Sundays). If you instead your first destination from Florence is Cortona, then you can take the train from Florence to Cortona-Terentola station and catch a shorter shuttle bus from there. If all this sounds too daunting, then a rental car for your time in small-town Tuscany can fairly easy and more certainly more flexible.

My suggestion is to rent a car for your travel plans. Colle VE is very small and quaint town but after a few hours you'll have seen everything you can possibly see in town. With a week at your disposal, if you have a car you can visit numerous towns nearby (Siena, Volterra, San Gimignano, Monteriggioni, Castellina in Chianti, Certaldo, Pienza, Montepulciano, Montalcino and many more, all located within 30 to 90 min drive from Colle). Without a car you'll have to rely on not so frequent bus service to see those small towns and private car transfers (taxi) are really expensive.

If you absolutely refuse to rent a car, then you have only 2 options:
1. A private car transfer (expensive but more comfortable than a bus)
2. Taxi or Volainbus from the airport to the Florence station, then a bus from via Alamanni (next to the train station) to Colle Val D'Elsa.

From Colle V.E. to Cortona the easiest way is with a car. If you rented a car, as I suggested, you can be there easily in about 1.5 hours. A private car transfer will also do the trick, but at a much higher price.
Using public transportation, you need to take the bus back to Florence, then in Florence you take a train to the Cortona-Camucia station.