I'm a big fan of Austria and Salzburg is my favorite city that I know. It's a great walking town, in fact I've walked the entire top of the Mönchsberg, the mountain the castle sits on. Wonderful views of the city and behind the city where you actually can see the real mountains. For the kids, the castle is great ... just the hugeness of it is worth seeing. Take the Bahn up and walk down. Go to the Marionette Theater ... it's absolutely awesome! Well worth the time and money. Hellbrunn Palace would be great for the kids, especially the tour through the "water gardens" ... where they're likely to get a surprise shot of water from a deer antler or a stool. There's a magnificent "machine" that they would be fascinated by. Mirabell Gardens is always worth a visit, especially if you've seen Sound of Music ... the kids could dance under the arched greenery singing do, re, me. :-)
Eagles Nest is worth seeing, in my opinion, but the house, Kehlstein, can only be visited if you eat there, as it's a restaurant. But the bus ride up the mountain, the elevator, and the spectacular views are great. A lot of history down where you buy bus tickets and would suggest seeing the bunkers.
Dachau ... I guess it depends on how interested the kids are in history. It would be good to walk the grounds, see the barracks, the ovens, etc. The museum has tons of displays and it takes a long time to read everything and look at the displays. But if they're interested in it, maybe a quick walk through, picking out a couple exhibits that they should see/could handle, might be good.
Just a few miles from Innsbruck is the Swarovski Kristalwellen ... their museum. I thought the $20 entry fee was a bit stiff, until I got inside. Your kids would love it ... animals made of crystal, an entire bearing wall of the buidling is lined in crystal; there's a room that's like a geode and you can see yourself everywhere you look. Lots of reflection exhibits and just a really really fun museum. Well worth the price.
If you like oompah music, go to Zillertal ... it's a valley about halfway between Innsbruck and Küfstein that has all kinds of oompah bands. They even televise shows from some of the locales. And it's beautiful! Though it sounds like you're time might now allow for that. But wanted to throw it out.
Enjoy! No matter where you go in Austria, southern Germany or Switzerland, it's all like eye candy. And smart to stay in one place for a few nights, especially with kids. Take time to get out of the van and just walk to a stream or up a hill to a cross ... enjoy the beauty of it.