Easy answer here:
Take the A22 autoroute from Verona Northwards past Trento and upto Bolzano. Literally just past Bolzano you will go through a tunnel and just after the tunnel you wlll see the Bolzano Nord junction exit. There will also be a large sign with the road names of various Dolomite valleys such as Alt Sciliar, Val di Tires, ALpe Di Siusi etc. The junction exit is 500m from this sign. Another sign just before the exit reads "Bolzano Nord, Vald'ega. You need to take this exit!!
Once you take the exit you need to pay the road toll. Then you will come upon a junction where you can turn left or right. You need to turn left. Keep following the road for several miles till you come to a village called "Blumau Prato Isarco". Drive through the village and do not turn off anywhere. The road will then split and veer to the right and you will come upon a tunnel. At the tunnel you have two lanes, you want the left lane for Tires/Sieser Alm.
Now you will start spotting the signs for castelrotto which will be approx 17km away. and you will start climbing. Keep following the signs for Seiser Alm/ALpe Di Siusi and Castelrotto. You will pass through the villages of Fie Allo Scilliar, Siusi and then you arrive at Castelrotto.
DIrections may sound complicated but they're not! Just wanted to point you to the correct Autoroute exit and onto the correct road after the exit. After that you just follow the road and the signs and do not have to turn off anywhere.
I have not been to Lake Garda but hear its very nice. You could easily make a detour to it as the Eastern shoreline is close to the A22 autoroute. I have no idea what to recommend though. best to ask on the appropriate forum