You're right, many of the private tours have vans that go up to 8 guests and that's it. But most agencies have more than one vehicle so it is possible you could book both the van plus an additional car for the extra 4 people.
So you have two options: first one, contact an agency directly to book for the entire party, with a van and an additional car to have the remaining 4 people all go to the same location.
Second option is to book dinner separately from the transportation (they are called transfers here). You book the dinner directly with the winery, but you can also ask whether they can arrange transfer. Some might be able to arrange the transfer to get to them or not, you can always ask.
In any case, if not, then you go about setting up transfer separately.
For this second option, I am making several recommendations below of wineries that offer dinner with links to their usual "offers" but my main recommendation is to actually contact them directly and find out whether they can offer the private dinner for your entire family and also ask about transfer services, then if not, we can then focus on getting a transfer as a separate thing, especially if you really like a specific winery.
- near Vinci - https://www.villadianella.it/il-ristorante/
This is my first recommendation because I've been there and seen the environment. They have a lovely winery and restaurant directly in the winery
and dinners are offered by booking. It isn't too far from Florence, you can actually take train to Empoli and just arrange for transfer from there to the villa. Contact them and ask them if they can do the transfer for you as part of the dinner, at least from the train station; there are trains until late evening.
They have a large garden outside around the villa so if kids want to roam, they definitely can. Elegant but not presumptuous setting.
Castello Vicchiomaggio -
Greve - https://www.vicchiomaggio.it/eng/greve-in-chianti-hotel-and-winery
I've also been to this place and it is a beautiful estate just off the main road between Florence and Greve in Chianti. If it was a lunch, you could even get there by bus.... but the last bus back to Florence is around 8pm so it doesn't work for dinner.
In any case, it isn't too far and they also offer dinner upon booking, so check it out!
- Radda - https://albola.it/en/experiences/
This has several options for wine tastings + winery tour + lunch or dinner or just dinner.
I think the first 2 are for lunch, the second 2 options are dinner. They also offer cooking classes which then turn into dinner, but might not be an option unless the kids are all at an age where they might enjoy it. You'll know if that fits for you or not.
Osteria di Passignano
- near Greve - https://www.osteriadipassignano.com/en/osteria-en/#menu
If you want, they also offer "experiences" that include wine cellar tours or cooking classes.
I'm putting this together with Antinori as they are part of that family and Antinori has another restaurant at their main winery in nearby Bargino
. The Antinori empire has grown and the winery at Bargino is a special experience but, considering you have kids, I would not recommend the restaurant there at the winery for them. I would say look into the Trattoria della Fonte
which is nearby in the countryside, considering it will be July you can eat outside, the atmosphere is elegant but more laid back so if the kids want to get up and move around you will feel fine without worrying. Here's the link for that restaurant - https://fontedemedici.it/it/trattoria-della-fonte.html
Castello di Verrazzano
- Greve - https://verrazzano.com/prenotazioni-visite-guidate/booking_2/?lang=it-it
Also offers an option for dinner, but seems to be only on Saturdays, and lunch on Sundays - just double checked your dates and that won't work, but you don't say whether you are somewhere else nearby before your stay in Florence so it might still be an option....?
- San Gimignano - Now this place offers lots of options for dinner so maybe this can work out for you if the above don't.
Check out https://www.torciano.com/en/visit/dinner/
- they actually have a package that includes transport from Florence but I would suggest you contact them directly and see whether they can personalize the offer for your group, considering you might have kids that might not be eating as much as an adult you shouldn't pay for an adult and that way you can actually ask for a special menu for kids.
Querceto di Castellina
- Castellina - https://www.quercetodicastellina.com/en/food-and-wine/wine-tasting/
The last option on this page is a dinner in the vineyard... it would be a private dinner for you, considering you are here midweek and do have the minimum of 12 people for the event, maybe it is something you can consider? You'd have to contact them as it would be considered a private event planned just for your family.
Okay, I hope these suggestions get you started! Let me know how things progress and if you need more suggestions. Also make sure to tell them all that I recommended them to you (Lourdes from DiscoverTuscany.com) because some of them know us and any personal connection you can make direct with them makes a difference!