12 days in Italy in June - itinerary recommendations

Stay in Florence
No need for a car
You might have too many day trips planned from Florence

Probably not enough time in Venuce
How many nights on the ground in Italy is this trip?

What time is your departure flight?

Do you have a guidebook?

Are your flights already booked? If not, it would make more sense to fly into Venice and out of someplace else, such as Rome. That way, you don't waste time and money backtracking.

In Venice, we stayed at a suite we booked through Residenza de'l"Osmarin. https://residenzadelosmarin.com We had the Valentine Suite and loved it, although for your teens, it would mean sharing a double bed in a low-ceilinged room. The location was perfect, though--overlooking a quiet canal but very close to St. Mark's Square. They have other suites with more beds, if that's what would work better for you. Be aware that these are self-catering suites, and these aren't hotel rooms, so there's no concierge or housekeeping, if you want those things.

The night before our early flight out, we stayed at the Best Western Titian Inn Airport hotel. They have a shuttle to the airport (for a fee), but the bus also stops right in front of the hotel. They also start serving breakfast very early (4 a.m., if I remember correctly), if you have an early flight.

In Rome, we also stayed in a suite, which we booked through Incentrum. https://incentrum.it/en/home-page/ It was large and conveniently located (not far from the Spanish Steps). If you book here, it's good to know that only one of the buildings has an elevator, and the other can have a lot of stairs, depending on which suite you book.

There are both beaches and hot springs not far from Rome, but I'll leave recommendations for others who have been to them. We were there in November, so we didn't go to a beach.

12 days is not specific enough. Do they include the arrival and departure days? That is why we need the exact number of hotel nights you will be on the ground.

If you can, change your flight to a multicity open jaw flight, where you arrive to Venice and return to the US from Rome. If that option is not available or prohibitively expensive compared to going back by train, the do the following.

Arrive to Venice airport. Immediately head to Rome on the same day if your flight arrives in the early afternoon or earlier.
Assuming you have 11 nights on the ground (if it’s actually 12 nights add one where you want, probably Florence if you want more Tuscan day trips. Bologna is not in Tuscany but only 35 min away from Florence cia high speed train).
Stay in Rome 4 nights
Train back to Florence
Florence 4 nights (take one or two day trips max)
Train back to Venice
Venice 3 nights
Fly home.

If you can change flights to open jaw multicity (arrive Venice return from Rome).
Arrive Venice
3 nights in Venice
train to Florence
4 nights in Florence (with 1 or 2 day trips)
train to Rome
4 nights in Rome.
If you can change flights the latter option is preferable because you save the time backtracking back to Venice. The train journey from Venice to Rome (or viceversa) is 4 hour long and costs 99€ per person for full walk in fare in standard (economy) class. Therefore even if the open jaw flight will cost you $120 or more it would be cheaper in the end.

I'm planning a similar length trip with my family of 4 w/ two teenagers, planning to fly into Venice, train to Florence, drive to Bologna, drive to Italian Lakes, fly out of Milan. Might Rome be a bridge to far this trip? I know, I'm struggling w/ the same issue of a rare trip to Italy and not going to Rome. But I'm finding plenty to do in between.

The train from Venice to Rome is 3h40m. Factor in time to get to train station (and get there early), checking in/out, etc you're looking at least 5 hours devoted to just get there.

If your kids love water, and you're bound to Venice airport coming and going, why not consider Lake Garda? Then maybe Bologna w/ your base and one (long) day trip to Florence?

Bologna area has numerous exotic car museums, including a Lamborghini factory tour. Your teens might be interested in that.