How to reach Dolomites and then travel to Austria from Dolomites

1. Go to Val Gardena. I prefer it to Cortina, but it will also be much easier to reach and then get to Innsbruck.
2. There is a direct Frecciarosso train from Florence SMN to Bolzano every 2 hours at 36 past the even hours.(8:36, 10:36, etc.) Takes about 3 1/4 hours. At Bolzano change to the bus to Val Gardena, taking about 1 hour.
3. Frequent connections to Innsbruck by taking a bus that connects to local trains to Innsbruck with a few train changes on the way.

You can look at combined bus and train schedules at https://www.suedtirolmobil.info/en/
Just put in start point and destination, date a time of travel. You might start with Ortisei Plaza S. Antone as a location in Val Gardena.
Use Bozen, Bahnhof Bozen for the train station in Bolzano, and Innsbruck Hauptbahnhof for destination in Austria.

Use https://www.trenitalia.com/en.html for schedules from Florence to Bolzano. Use Firenze S, M. Novella as the start station in Florence.

If you opt for Selva Val Gardena, when you depart Florence, I would suggest taking the train to Bolzano. High-speed Frecciarosa trains complete the journey in 3.25 hours. From Bolzano, local Bus #350 travels 55 minutes to first reach Ortisei and then continues 20 minutes more to reach Selva Val Gardena. Bus 350 stops near Bolzano’s train station before continuing to the Dolomites.

After your stay in the Dolomites, you can return to Bolzano by bus and then take a two-hour train from Bolzano to Innsbruck, Austria.

Depending on how much time you are looking to spend in the Dolomites, a rental car could be an option if your goal is to visit throughout the area. There is a to-rent office near the station, if memory serves.

First, it has been a LONG time, but when my husband and I went to the Dolomites, we thoroughly enjoyed Castelrotto. I'm actually sending my sister and brother-in-law there this coming September (I'm planning their trip to Italy since they've never been and I've been 3 times). I haven't gotten to that part yet in planning, but they will be heading from the Cinque Terre and taking a train to Bolzano and from there catching the bus to Castelrotto. The town itself is absolutely charming and the available hiked are wonderful.

For question 2, there are a lot of options, because things are a bit unclear. However, in Italy, take the train! At least take the train from Rome to Florence and then to the Dolomites. Are you wanting to rent a car? If so, you could rent one in Bolzano and continue the rest by car. If you are looking to avoid that, most all places are accessible by train, and if not by train, then by bus. The Dolomites are very drivable. My husband declared that's the ONLY part of Italy he will drive! Anything south of Milan is just too busy and so easy to navigate by train anyway. Austria is also easy to drive.

Personally, we'd drive from the Dolomites to Austria but trains are just as easy, though I've never taken that exact route. Are you sure Innsbruck is where you want to go to? Don't get me wrong, I enjoyed Innsbruck, but Salzburg is stunning. It's a two day drive from Salzburg to the Dolomites, that I know; I don't know how long a train would take. If you drive, stop in the tiny town of St. Anton, Austria, as the mid-point. I fell in love with this town and was sad it was only a one night stop. Absolutely breathtaking!

If you have any other questions, about Italy or Austria (which I haven't gotten to explore as much), please don't hesitate to ask. How long is your total vacation? I'm just curious because you are definitely trying to squish in a lot of traveling. I'm all for that (trust me, when we go to Europe we see as much as I can possibly fit in), but knowing how long you have could help me with my recommendations.

Thanks for the detailed answers. Is there any particular recommendations for Dolomites. I will be there for the first time and not more than 2 days.

Any recommendations of which Car Rental should I take in Bolzano?

Ortisei is a great location with easy access to the lifts to the Alpe di Siusi for hiking.
The bus and train systems are wonderfully integrated in Suedtirol. Only the Swiss do it better (and maybe Netherlands, but they don't have any mountains).