Hi Pat,
We did the same drive, over the course of 4 nights. We drove from Berchtesgaden, over the Grossglockner, and stayed one night in Heiligenblut. Very pretty and extremely scenic village. Next day we drove via Cortina (didn't care for Cortina) and then to La Villa, in the Alta Badia, which is about an hour west of Cortina d'Ampezzo. We stayed in La Villa for 3 nights and then headed to Hall in Tirol for a few nights.
The Alta Badia has some of the best scenery in the Dolomites. Dramatic limestone peaks just spread out if front of you.
The drive from Salzburg to the start of the Grossglockner Hochalpenstrasse (at Bruck an der Grossglockner) takes about 1:30 hours to get to. Figure the Grossglockner Road is basically between Zell am See and Heiligenblut. The drive over the Grossglockner can take an hour or as long as you like, depending on what you want to see and do along it. The actual pass (road) is not that long.
Going from Salzburg over the Grossglockner to Lienz to Cortina to Bolzano to Innsbruck is over 9 hours driving, non stop. Not stopping at all for anything. Figure on at least 11 or 12 hours with some stops, especially along the Grossglockner, and to eat for for other things. To suggest that 9 to 12 hours of driving is a full day is an understatement.
There is no need to drive "The Great Dolomite Road" as laid out in books. That would be a waste of your limited and valuable time. I wouldn't bother driving to Bolzano, which is a city which is not even in the Dolomites. From Cortina, simply head west through the Alta Badia (San Casino, La Villa, Colfosco), then over the Gardena Pass (even more stunning drive than the Grossglockner Hochalpenstrasse) into the Val Gardena (Selva, St. Christina and Ortisei) and then north to the Innsbruck/Hall in Tirol area. I have to say when approaching the Innsbruck area from Italy on the A22 highway, the high alpine scenery is simply amazing to see in person. Unforgettable.
Ok. I'd plan on at least 1 night, but 2 nights would be better along this route. Just to get to Cortina d'Ampezzo, without stopping, will be 4:30 of driving. To get to my recommendation of the Alta Badia for a night would take about 5:30 non stop driving. If that's doable, then you could plan on 1 night on this trip. I'd allow two, as it would be more relaxing, and the extra day gives you a better chance at some clear weather.
http://www.altabadia.org/en/summer-holidays/summer-in-the-alps.html
http://www.val-gardena.com/en/summer-2015/page28.html
Paul