Tuscany/Dolomites and Ireland

Unless you don't plan to ever travel to Europe in the future (and there is no reason to think that unless you don't think you will survive another year on this planet), my recommendation for a two week trip is to concentrate on one country only. Two weeks aren't even enough to scratch the most basic famous destinations in Italy, let alone two countries at the opposite side of Europe.
I have a friend in Florence who is married to a Hawaiian whom he met when he was living in Honolulu for a short stint. They come to Hawaii every year and his flight of choice is out of Florence (FLR) with Lufthansa/United (partners with the Star Alliance) via Frankfurt (or Munich) and San Francisco. He generally stops at least one night in San Francisco where his wife has family, but I think it's possible to do it all in one shot if you fly via Frankfurt.(the Munich flight arrives to SFO too late in the evening).

We're planning a trip to the Dolomites in June, and advice on this forum has been to rent a car in the Dolomites if you are time-constrained. Just an FYI that you can't rent a car between noon on Saturday and Monday morning in Bolzano or Trento. You can rent a car during that period in Verona at the airport.
Verona also seems to have good flight connections via Lufthansa to Frankfurt as well, which we're doing to save some backtracking/time since the Dolomites are at the end of our trip.

Its your vacation.
My suggestion, for what is is worth, is to buy round trip tickets to Dublin. That looks to be $1500 pp. Go see the west of Ireland, although without a car I don't know the logistics. Then fly Ryanair (yes, them) Dublin to Pisa and train to Florence. From Ortisei, bus/train to Bergamo and fly back to Dublin on RyanAir, spend the night in Dublin, then fly back home. The Ryanair flights should be in the 100 euro pp with luggage fees.
With 2 nights in San Francisco (or 1 night and a red-eye) plus a red-eye and a night in Dublin, that gives about 4 nights in Ireland on the way over, then 7 nights in Italy.

Thank you all for your suggestions. I will put Ireland aside for the moment and get input from that forum. Any suggestions for places to stay in Florence? Also - is there only one train to Bolzano? We would like to see as much scenery as possible while traveling. There are varied opinions on which village is nicest(Ortisei, Val Gardena) they all look beautiful to me. Simple, "R.Steves" type hotels are fine for us - we want to be close to everything and soak up the views!

There are lots of trains to Bolzano, but you might have to change trains along the way. Do not use Raileurope to check schedules, use www.trenitalia.com, the Italian state Railway. They run the trains.
Bus schedules in Alto Adige/Suedtirol, https://www.sii.bz.it/en/fahrplan-orario-orar-2016
Val Gardena is a district. Ortisei is a town, along with Santa Christina and Selva, in the Val Gardena. Ortisei is best for access to the Alpe di Siusi plateau of alpine meadows and hiking, IMO. Beautiful town.
Since the area is trilingual, Italian, German, Ladino, I could also refer to it as St Ulrich in the Groedental, with access to the Seiser Alm. Don't ask me what it is in Ladino, although Ortisei is a Ladino name.

Two Ortisei hotels/B&Bs to recommend from personal experience: Hotel Garni Walter and Villa Aurelia. Each will give you a bus pass for all bus travel in the area for the duration of your stay. You will want to buy a Val Gardena Pass for the lifts.l