The person around here with the clearest idea of satisfying places is, I think, Sandralist and I hope she returns with some suggestions for you, given your clearer criteria. She lives there, if she's who I think she is, and from what I can discern, is particular about where she goes and isn't shy about saying why.

I think you have to decide how much you're willing to adapt/sacrifice your family's vacation to the needs/interests of the grandparents. Unless you're wanting to have some time when all 6 of you are together, I would spend a week with one grandparent, a week on your own, and then a week with the other grandparent. Hopefully, the destinations you choose for each grandparent will also be places that the members of your family will enjoy.

It is not clear to me if you plan to have a car for most of the trip. Also, I am wondering if it is possible to flip the order of your trip so that you end in the Dolomiti, to give yourself a chance at (maybe) cooler weather at more destinations in the lower elevations. earlier in July. That said, you can get a heat wave anytime and anywhere in summer in Italy, so wherever you go beyond the Dolomiti, you should get air conditioning.

I am sympathetic to your desire to stick to 2 extended locations but it is hard to think of what to combine with the Dolomiti that would provide almost 2 weeks worth of interest and which is also not too hot and not crowded in July. Keeping your small kids amused shouldn't too difficult anywhere if they have some place to play and you have small budget for toy purchases. I am bit more concerned about you and Grandma getting bored.

A garden apartment in Peschiera del Garda might work, because it is a 30 minute train ride from there to Verona, plus there are boat rides to Sirmione and Bardolino (crowded on weekends in July!), plus the amusement park of Gardaland could be a big blowout for the 6 year old for at least one day. Pescheira del Garda is really very much a family destination, for feeding the swans and playing on swings and pedal boats and eating incredible ice cream sundaes. If you have a car, you can do a few more day trips like Mantova/Sabbioneta or Vilaggio sul Mincio.

If you and your mom liked the Riviera, only le Cinque Terre and Portofino are unbearably crowded in July. The towns I mentioned above are not crowded and are filled with lively shopping, and also have quite cool and shady, breezy streets away from the beach. You can take boat rides and train rides. A willingness to stay in a large modern apartment rental in those towns would really expand your options (and net you air conditioning.) If you have a car, then you can consider staying near Lerici, which has no train station but which is much closer to Tuscany, and then you can consider some car day trips to Pisa and other Tuscan towns. Lerici has an adjacent town -- San Terenzo -- which might be a bit better (flatter) for kids and people who don't like stairs, but finding an apartment could be a challenge. It is just not known to tourists.

http://www.nytimes.com/2010/06/20/tr...anted=all&_r=0

http://www.santerenzo.eu/index_en.html

One last suggestion is to look in the small Tuscan town of Pietrasanta and the Lido di Pietrasanta, which is along the coastal train route between le Cinque Terre and Pisa. It would be best to have a car there, but you can get by with using the train to visit small towns of interest plus have a lot of beach time. I would expect it to be more humid and less breezy than the Riviera, however.

If you can combine air conditioning with a willingness to live like Italians in July -- early morning activity, heading indoors for food and rest in the long middle of the day -- re-emerging around 5pm for gelato and more activity until dinnertime, and then relaxing outdoors until bedtime -- then the range of possibilities of where to go opens up, even if they are hotter, and most especially if you have a car. But in general, Italians themselves like to head to the mountains and seaside as much as possible in summer, and it is fun to join them there if you make a point of avoiding the famous international tourist destinations.