In Florence, walk or drive from train station to Hertz Via Borgo Ognissanti

Because of the closure of the Amerigo Vespucci bridge, driving out of Borgo Ognissnati without serious ZTL issues is more complicated. There are also restricted bus lanes where fines can result. I suggest you change the pickup to Via Palagio degli Spini, the complex near the airport, reached by taxi. The fare will be €22 plus a small baggage fee. Read this about driving in Italy and restrictions involved; avoid leaving anything of value in a car when parked:

http://driventoit.blogspot.com/

Be sure anyone driving has an IDP.

Only you can make this decision. Google maps shows a distance of 650m (less than .5 mile) to the car rental; that may be more or less, depending on which train station door you exit from.

I wouldn't want to have to drive a car back to the train station, that would be a hassle.

How many adults vs. one 2-year-old? How much luggage? Is it wheeled luggage? How far can the 2-year-old walk? It might be good for the active 2-year-old to walk for a bit, it might tire her out a bit. Yes, it's a city, with city traffic, but other than having to hold the 2-year-old's hand (which I hope you would do on any city street, in any city), I don't think that would effect the walk from the train station to the car rental place that much.

The easiest solution, if you're concerned, would be to put the child and a couple of adults and some of the luggage in a cab, and have the cab meet the rest of the adults at the car rental. (It may take longer for the cab to get to the car rental location than it does to walk there.)

I disagree with the first reply. Going to the airport is unnecessary waste of time and additional expense (taxi plus airport extra rental charges).
Getting out of the Garage Europa on Borgo Ognissanti, where you pick up the car, is just as easy as previously. The bridge has nothing to do with it. You don’t have to cross the Vespucci bridge at all.
You can drive west to via il Prato. Then you can turn right (north) on Via Rucellai and west again (left) on Via della Scala. At the light at the intersection with Viale Rosselli you then turn left (as I imagine you want to go to the A1 freeway).
Although the Vespucci is still temporarily closed southbound (it’s open in the northbound direction since yesterday), you can still cross the Arno river if you want. Because of the bridge closure the ZTL camera at the intersection of the bridge and Lungarno Vespucci has been turned off. So now to cross the Arno southbound you take Lungarno Vespucci eastbound to the next bridge (Ponte alla Carraia) where you turn right (south), cross the bridge, then right again (west) on Lungarno Soderini and there you are on the south side of the half closed Vespucci bridge.

Parts of Florence's historic center have no sidewalks, or not of useable size. However, if you follow the Google Street View, I think you'll find they're routing you on a street that has them! I'd still strap the child into a carrier or stroller, if you're bringing one.

I would not bother to drive back to the station. That would be a hassle for the driver. it is possible to drive back however (from the previous directions you’d turn right on Viale Rosselli then right on Via Jacopo da Diacceto, along the light rail line. But as I said it’s not worth it. The driver might get tangled with all the buses and bus lanes there.

I don’t know who told you about the traffic but it’s not true. You will be able to walk to Hertz with no problem. Just be careful when you cross Via Alamanni on the west side of the station, as it’s a busy street with buses and light rail. Once on the other side of the street go to the right to Via degli Orti Oricellari (which further down becomes Via Santa Lucia). Turn left on Via degli Orti Oricellari then walk straight all the way till you see the BAR CURTATONE. That is the corner with Borgo Ognissanti. The Hertz office is almost next to the Bar Curtatone (a few doors to the left). There is no significant traffic on Via Orti Oricellari or Santa Lucia as it is ZTL area, however via Santa Lucia has narrow sidewalks.

Roberto is correct of course as to the route, but the problem is knowing where you have to turn before getting to an intersection. That's what I meant by being complicated.

As Roberto says, the walk is not long. As for driving to the station, the point is that you are renting multiple cars. Unless you use the underground parking, there is very scarce parking place on the Alamanni side of the station and you can't stop a group of cars there waiting for people without causing a traffic jam.

Another possible idea could be taking the T1 tram from the Alamanni stop to Sansovino and rent from the Hertz agency there. It would be easy unless you have plenty of luggage.