In reply to Sealwife:
You've certainly picked places off the beaten track!
Pieve di Cadore, its been a very long time since I was there. It on the main drag to cortina, and you have Antelao, Sorapiss and the back of pelmo close by. Plus the Friuli Dolomites. All of these as less well travelled areas with far fewer foreigners, more Italian footfall.
San Martino as someone has already said has the Pale di San Martino to the east, but also the less known Lagorai massif to the west. Although I've not explored it in a meaningful way, it's very beautiful and different from most of the Dolomites in that it is an area of granitic rocks and it feels far more like Scotland, with lakes and ponds rather than the more arid limestone areas.
Cenchenigue is a bit of a sleepy place. It's sandwiched between the ramparts of Civetta and the Pale di San Lucano in a deep valley. Walks will be high elevation unless you drive. But you do have some nice stuff around you. Civetta is stunning, and you can access the range from Val Corpassa or from Alleghe. Ot there is a hard VF (think is called Fiame Gialla) which climbs the vast wall directly above the town. You also can go west to Falcade where you can walk on col margarita or on the northern side of the valley towards Cima d'Auta. Quite green and rolling terrain until you get high. Or there is Val di Gares which accesses the southern side of Pale di San Martino. Quite an impressive cirque. Looking south there is Moiazza, give hard VF on that, or monte agner. This presents the largest height gain of any valley in the Dolomites, its a pretty wild place and not well known. Also Agordo is the local main town and nice for a potter. North you have Alleghe which is a nice town by a lake with pedalos an ice rink and restaurants.
Igne I personally wouldn't bother with. Too low and isolated from the main mountains. You'll be driving all the time and the drive to passo staulanza where you can get to pelmo is long and windy. Just too far out of the action.
Same goes for velturno really. It's a motorway exit primarily. To get there from Venice you'd have to bash motorway for maybe 4 hours? You'd be better off flying to Verona or Innsbruck. But even then you'd want to drive into the mountains which will inevitably lead you to val gardena which will be heaving, and to get to the good bits, that will mean sitting in traffic. That said the western Dolomites are beautiful, as long as you ignore the crowds.
Arabba is a small ski town. It's pretty and high up. Have lots going on around you, mtb on the sellaronda, various vf, nice walking around settsass and col di lana with incredible history. If it were my money, for a family holiday with mixed abilities and interests, this is where I'd go. This or Alleghe rather than Cenchenigue. I'd point you at my apartments but we're fully booked around then. Good luck and if need more help, let me know.