The Dolomites are geologically and geographically distinct from the Alps of Austria and Switzerland, being composed of Dolomitic limestone derived from ancient seabeds rather than granite and metamorphic rock. Most locals and other “mountain people” reserve the term Italian Alps to refer to non-Dolomitic peaks more to the west, around the Val d’Aosta and Gran Paradiso National Park,and to the north in Stelvio National Park.
https://wineandtravelitaly.com/gran-paradiso-national-park/
https://www.parconazionale-stelvio.it/en/stelvio-national-park.html
The Dolomites themselves are divided into the eastern Dolomites, east of the Adige River, and the western or Brenta Dolomites to the west. Just north of the Brenta Dolomites is Stelvio National Park.
All are spectacular, but without a car the easiest to visit by far are the Dolomites east of the Adige. These are the “classic” Dolomites, and what most people here (including Rick Steve’s himself) are referring to when speaking of the Dolomites. This region has excellent tourist infrastructure and is very family-friendly.
For a town to stay in for 5 nights, in a vacation chelate or apartment, I will suggest the town of Ortesei in Val Gardena. There are lifts that ascend both sides of the valley to the hiking trails. Alpe di Siusi on the south side is a high meadow with lots of nice rock-free trails. We have had a great time up there on mountain bikes.
We are returning there next summer with our 11-year old grandchildren.