Our family (2 adults, 2 teens) went to that Sommerrodelbahn in 2018 and we all loved it! You could take the train to Hallein, then the bus. I know that the bus goes on that road (I remember seeing buses stopped as we drove along there a couple times) it’s just a matter of figuring out which ones. It’s very close to the salt mine, so their website may give you some direction. If not, contact the visitor information center for Hallein.
I’d also recommend the Red Bull museum near the Salzburg airport. My teens loved it. And it’s free to get in.
We went paragliding over Salzburg with FlyTandem and it was absolutely amazing. My youngest was 12 at the time.
Werfen fortress just south of Salzburg is great, especially on the days when they have the falconry exhibits. And there is an ice cave nearby. Not sure how accessible it is, as we had a car. But both would be worthwhile.
Stop for bread at the nunnery in Salzburg (Stiftsbackerei St Peter) near the water wheel. My boys still talk about how amazing the bread is.