Some years ago, when my kids were the age of yours, we did Vienna(4)-Budapest(4)-Plitvice Lakes(1)-Split(3)-Ljubljana(3)-Salzburg Country(3)-Vienna. We did 3.5 weeks (if you could extend a little, that would be good).
We really enjoyed Vienna - we went to the heuriger pubs (wine gardens) along with museums. We rented a car to go to BP, PL, Split, Ljub, and back to Vienna - with 5, it was much cheaper. We had a great time in Budapest, went to the baths and House of Terror. We then traveled to PL - had lunch in Zagreb. The trip B-P->Zagreb was about 5 hours - we had breakfast on Lake Balaton.
We spent 1 day in PL, then on to Split. Really nice there - good restaurants. We stayed in a sobe (Croatian B&B). These are very pleasant vacation apartments. After a few days there, we started back and stayed in Ljub - Hostel Celica (old commie-time prison). Ljub is a great small city. We then went to Salzburg area, but stayed in the country, and never got to the city. We stayed in a agrotoursimo - farm place, which was a ski chalet but a vacation house in the summer. My 22 YO kids loved the chickens and animals. We then went to LInz and Mauthausen Concentration Camp. I recommend this. It is a sobering place, but we must never forget. Then back to Vienna to return the car without a charge.
We planned all stays in advance. We didn't stay in hotels. We stayed in apartments, using booking.com or other services like that. We managed to find apartments for each stay for under $100/night. I think that's still possible, but will take some work. As to food, we seldom ate the hotel breakfast. Today, I think we would - you can get by most of the day by the hearty breakfast.
You should also consider hostels. Most hostels have private rooms. For Munich, look at 4you hostel. Close to the train station, with lots of bus lines. Also lots of German kids for your kids to meet at breakfast or dinner.
That was our trip. If you could add a few days, and cut out B-P, you could do something similar.