Are you taking the via Chiantigiana (SR222) from Ponte a Ema to go to the Chianti? Or are you going to Greve through the Passo dei Pecorai (from Il Ferrone)? Where is you daughter staying downtown exactly? Or any place downtown will do?
For now I will presume only you are coming from the Firenze-Mare freeway (A11), which certainly takes Empoli out of the picture.
This is what I would do. Coming from A11 at Firenze Nord Exit junction follow directions to A1 ROMA. Exit A11 enter A1 to ROMA. On the A1 you will go through the following freeway exits: FIRENZE SCANDICCI, FIRENZE IMPRUNETA. Exit at the next: FIRENZE SUD. Pay toll at the booth and immediately after the toll plaza veer to the right and take the Via Chiantigiana (SR222-Strada Regionale 222) in the direction of Siena, Ponte a Ema. As soon as you turn right there is a huge Sheraton Hotel on the right. Stop there. There are probably taxis in front, if not get inside and ask the desk staff to call a taxi. Put your daughter and friend on the taxi to the city center and send her on her merry way. It won't cost more than €20. Actually the Sheraton even has a free shuttle to the city center (although I think it's for guests, but who is going to check?).
You and your spouse get back on the car and proceed on the same road toward Siena. The Sheraton is the beginning of the Chianti road.
Simple, comfortable for everybody and no grudges. Any other advice given to you so far will cause you to stress out at the wheel driving in the city and your daughter will likely put you in a rest home where they beat up old people.