I think your itinerary looks good, especially if you fly "open-jaw"--into one airport (Milan) and out of another (Venice.)
We did something similar last May. We arrived in Varenna by train, having switched in Milan from Naples. When leaving Varenna, we took the train to Verona to spend a few days, then picked up a car. We drove up to Bolzano and stopped to visit, then continued on to Ortisei. Heading home with a flight from Venice, we drove from Ortisei to Venice; through the mountains. If you chose to drive, you could take the train Varenna-Milan-Verona-Bolzano and pick up a car there, as someone else mentioned having done.
There are pros and cons to the car or using buses for the Ortisei portion, but I think either way would work for your family.
Driving gives you flexibility. One of our days it rained, and we drove to Merano, a town to the northeast (we had already stopped in Bolzano on the way, which would be another good choice.) Other than that we didn't use the car while in Ortisei because on the other 2 days we took the lifts to do hiking. The drive through the mountain pass to Venice, (and there are many beautiful ones to explore,) while spectacular, needs a driver who is ok sharing narrow roads with busses and bikes. My husband was Ok with that job. Alternatively, you can drive back the way you came, through Bolazno and Verona, on to Venice. There, we chose to stay just outside of Venice, very close to the airport at a place called the Venice Resort Hotel. The rates were reasonable and they had parking for the car. If the car was already returned, they had a shuttle to the airport. We didn't take advantage, but there is also a local bus that you can take to go into Venice for the evening, if you chose.
Using the buses while in Ortisei could give you flexibility if, for example, if one day the girls wanted to go one way, and you another.
Or, you could easily travel to another town to do hiking there. Then there are no worries about the car. i thought we would do more driving around than we did, probably because of rain for he first day and a half.
In Varenna, we stayed in Albergo Milano, which is well recommended on this forum. We met a family staying in an Air B&B who were happy with their choice.
In Ortisei, I would recommend staying close to the town center, rather than a bit up up on the mountainside, which we did. The return climbs were pretty steep each time we set out.
You didn't mention when you would be going, but lifts in the Val Gardena area of the Dolomites don't start operation until late May.
www.valgardena.it is helpful. Search for 'hiking' or 'summer.' You can find information on the refugees there, also. Dates for the lifts are in month/day order, not day/month.
If you are really interested in staying in the huts, or refugees, I would suggest starting a separate thread with that question, since there are people on the forum who have done that.
