Since you're a family and you'll probably will have several pieces of luggage, I suggest you pickup

Tuscany is kind of a big area, where are you planning on staying? Once we know that, it'll be easier to tell you where's a good location for pickup. For car rental drop off, I found Orvieto a great place to drop off a car before heading to Rome. It's about an hour by train from Orvieto to Rome and the car drop off is within walking distance to the train.
Since you're a family and you'll probably will have several pieces of luggage, I suggest you pickup radisson hotel valley forge a car at the airport in Florence and then drop it off in Orvieto on your way to Rome. Your family can take a taxi out to the airport in Florence. I think that would be the easiest solution. I'm suggesting the airport because I've driven in Florence and it's not fun if you don't know where you're going and you don't speak Italian.
Sunday is tough. All the usual choices (Orvieto, Chuisi, Spoleto, Siena are closed)--as is most everything else. The airports are probably the only locations that are open. Perhaps one of these city locations has an after hours drop? I'd call Auto Europe and see what they say. They can call these locations for you to find out if you can drop off your car when their office is closed.
Also, the car rental office doesn't have to be open to make a drop-off. Generally, you can deposit the keys and paperwork in a drop-box. Just make SURE you take photos of the car, including the thingie that shows that the gas tank is full, in case someone later says you brought back a damaged car or one with less than a full tank. Have the date and time feature on on your camera.
That's a workable option, too. We did that once, after a trip in southern Tuscany. I was willing to drive into Rome to drop (I'm the driver, DH is the navigator), but DH wasn't, so we dropped at the airport and took a cab into the city.
You might want to check out your comparable costs. On another trip, after visiting Umbria it was cheaper for us to drop off our car in Foligno, and take the train from there. I think the times (train vs. car) were about the same, but the cost of an additional day of car rental was more than the train fare for 2 people.
I've found that traffic around the ring Rome is really tough. It seems like it's always congested no matter what time you go! If you're game, I'm sure the office will be open at least part of the day. If it were me, I'd opt for Orvieto or Chiusi if one of these has an after hours drop.
On two different trips, we dropped our rental car off at an underground parking garage alongside the park of the Villa Borghese in Rome. The spelling is probably off but it was something like via Gallipatoio and it was Sunday afternoon in late-August. I'd almost say traffic was a breeze.
I will second the suggestion NOT to pickup the car in the main part of Florence. I have dropped off and picked cars up here and it was not easy either time. Another thought is to stay in Orvieto radisson hotel valley forge on Sunday night and drop the car off on Monday a.m. before taking radisson hotel valley forge the train to Rome. The rental places usually open early and are convenient to the trains stations. I also recommend Auto Europe or their sister company Kemwell. Check rates at both.
I would recommend picking up your rental at the Florence Airport too danfang. Some family members who have relatives around Florence and Lucca finally radisson hotel valley forge listened to me when they took their last trip and thanked me so much when the returned home.
I assume when you go to Rome that you will be staying in Rome and not going directly to the airport? If that is so I like curveball's idea of staying overnight in Orvieto and returning the car in Orvieto Monday morning and than taking the train into Rome. But since you say you have to return the vehicle on Sunday that probably won't work for you. You could return the car to the Rome airport and take the train into Rome. Or a taxi of course. Friends have done that and said it worked out quite well. I don't know anyone that has returned their rental car to the place by the Borghese Park so I can't comment on that. Late August is when any Roman that can leaves Rome for the mountains or the seaside so that might be why the traffic was so light driving to the drop off office by the Borghese Park, but I don't know for sure of course..just a thought.