As I understand it, you don't have a lot of planning time now because the little ones use up all your time :-)
Mid-October is a very good time for Italy, after the summer heat and crowds, still long days and summer hours for sights. Find the time for planning (maybe even ask the grandparents to babysit for a few hours each week. . . ) and you can save quite a bit compared to the cost of a tour.
With only 9 nights in Italy, you are wise to eliminate Venice (though it's almost my favorite city in the world). That leaves you 2 choices for flights, either round-trip Rome or open-jaw into Rome and home from Naples. Maybe you could even find flights into Florence and out of Naples. Just go with whatever is cheapest and the least plane changes. If you give us your home city, some of us may be able to give you more help on that.
Staying in a farmhouse is often difficult because of the lack of transportation. Renting a car will only add stress and expense. Florence is a fine place to stay, and you can arrange a tour. If you land in Rome, you can continue to Florence by train the same day. It's best to start your trip there since it's not a big city so it's easier to get over jetlag and soak up "being in Italy." 3nights gives you a full day for the museums and a full day for a wine tour. Add a night for a visit on your own to lovely Siena, or for more of Florence's gems.
After Florence you can go straight to Naples if you're flying out of Rome. If you take an early train to Naples and a late train out, even 1 night there will give you a few hours to see Naples, especially the National Archaeology Museum (allow at least 2 hours) when you arrive, and spend most of the next day in Pompeii. 2 nights is better. I can recommend a budget hotel very near the train station - not the most attractive part of the city, but very safe, and walking distance to the historic center and the top-rated pizzeria and bakeries.
Once you have your dates (presumably have booked your flights) and know how many nights you want in each place, you can buy deeply discounted train tickets. The sooner you do this the more you'll save. But don't panic yet! Train tickets are only on sale now till early June so you still have lots of time. The same goes for hotels, you can find more bargains if you book early. Many places still allow you to book with a credit card guarantee (no advance payment) and cancel without penalty until close to your arrival.
And of course, the Forum is here to give you suggestions and recommendations as you make your plans. Get copies of Rick Steves Italy Guidebook and Europe Through the Back Door. Try your public library - even if the books are several years old, they will be very helpful to get you started.
