Bolzano

Cortina and San Vito di Cadore are quite a long day trip from both Bolzano and Venezia. Depending on the route, call it about 2.5 hours each way from either starting point if you are driving. From Bolzano, you can easily visit the Val Gardena in the heart of the mountains, but for Cortina you probably should consider staying in Cortina. There are buses all over the region too, but they take time. A lot of time.

Maybe you can tell us why you want to go to Bolzano, Cortina d'Ampezzo and San Vito di Cadore in April. It's between seasons then, neither ski season nor summer activity time. You could probably hire a private driver, although a lot of the tourist services (restaurants, hotels, lifts) in the mountain towns will be closed or on very limited hours as they rest up between the two busy seasons. Many lifts don't re-open until June.

FYI, a friend of mine had to hire a driver to take her from Bolzano to San Cassiano, which is closer than Cortina. It was Euro 100.00 one way, and he was doing a favor for the hotel she was staying at. A private driver for a day trip like that is going to quite expensive.

Bolzano will be more-or-less business as usual as it is more of a city.

It would take 3 hours to get to Cortina from Bolzano with public transportation on the current schedule.
Train to Fortezza, change to train to Dobaccio, 445 bus to Cortina. First bus is at 7:01. Last return bus/train connection is at 7:05 pm. Suedtirol journey planner: http://www.sii.bz.it/en/

Due to other family commitments mid-April is when we can travel next year. We're starting in Sorrento and the Amalfi coast. Then Rome, Orvieto, Bolzano, Venice. We chose Bolzano because it seems more will be open here in April. One of my grandparents was from San Vito di Cadore. The area is unique. (We traveled to Rome, Siena, the Cinque Terre, Florence in May 2012)

One of my grandparents was from San Vito di Cadore. The area is unique.

Makes sense you want to visit there. You have the info, though, on day tripping from Bolzano. It is a long day trip. Perhaps you can swing an overnight there or in nearby Cortina d'Ampezzo to make it less of a strain. This is an instance where I think that a one night overnight might make sense. It looks beautiful. Might have to put it on my ever-growing list.

Since April is shoulder season, bus transport is limited. You might think of traveling to Cortina from Bolzano with your bags and spend the night. Without a car, you might need a taxi to get to San Vito, from San Vito you can taxi to Calalzo where you can get a rail connection to Venice. There may be buses running to Venice from Cortina. Hard to tell right now as it is a whole season away.

Edit-Looks like there is bus service from Cortina to Calalzo train station operated by Dolomitibus, line 30. It also stops in San Vito.
http://www.dolomitibus.it/dolomitibus/jsp/orari.jsp
I'd definitely email to confirm. Taxi is an option if all else fails.

Thank you for your help! A night in Cortina makes sense!

Since you will be staying in Bolzano, check out the "Otzi The Iceman" exhibit at the archeological museum. Very interesting and should not take up that much time. Google it and see what you think.

I second the suggestion to see "Oetzi" at the museum in Bolzano. Quite interesting.