Need advice for 16 day itinerary Austria, Budapest and Prague

You can complete the itinerary like this:

Day 1 to Day 5 : Budapest

Places of Interest to visit: - Buda Castle Hill, St. Stephens Basilica, Central Market Hall, Hungarian National Museum, Fisherman’s Bastion, Danube Promenade walk, Margaret Island, Heroes Square, Memento Park, City Park, and Opera House.

Day 6 to Day 12: Vienna

Places of Interest to visit - St. Stephen's Cathedral Church, Rathaus, and Naschmarkt market, Schonbrunn Palace, Belvedere Museum, Spanish Riding School, Donauturm (Viewing tower), Vienna Natural History Museum, Vienna State Opera House, take Danube boat ride, visit the Wachau Valley and Melk Abbey.

Day 13 to Day 16: Prague

Places of interest to visit - Explore the Old Town Square, Visit Prague Castle, See the Treasures of St Vitus Cathedral, Test yourself at the Mind Maze, Visit Petrin Hill, Stroll across Charles Bridge, and day trip to the town of Český Krumlov. Catch a puppet show in Prague at the National Marionette Theatre and Theatre Spejbla & Hurvinek which both offer popular performances. Kids will love that.

https://www.timetravelturtle.com/cesky-krumlov-czech-republic/

I suggest buying Rick's guidebooks for each city. However, you can also see prioritized lists of indoor sightseeing on our web pages such as https://www.ricksteves.com/europe/austria/vienna, under "At a Glance." Add in some time for city walks, such those described in free audio tours available under "Listen" on the same page.

I'm glad to see that you're flying in and out of different cities. The two train rides between the cities are easy and need not be purchased in advance. Both kids travel for free without a ticket. If you want to try locking in the adult tickets ahead for a discount, then you can find links and tips at https://www.seat61.com/trains-and-routes/prague-to-vienna-by-train.htm and https://www.seat61.com/trains-and-routes/vienna-to-budapest-by-train.htm.

With two little kids you cannot visit half as much as if you were alone. You should not drag the kids through all the sights like adults.

You need to do some research. Many venues have special attractions for kids. E.g. Vienna: In the gardens of Schönbrunn palace there is a maze and the world's oldest zoo, in the city center there is a hothouse for butterflies, the NHM (Museum of Natural History), the TMW (Museum of Technology), several indoor and outdoor playgrounds, etc.

Seven weeks planning for such a trip is not too much.

Thanks friends for the suggestions.
Do you suggest any rail pass that might help. We are considering the eastern europe rail pass.
For Austria itinerary, we are planning to spend 2 nights in salzburg also. Can you suggest if we can do some day trips from Vienna as we have total 7-8 nights for Vienna.

As I posted earlier, you can do a day trip from Vienna to the Wachau Valley to visit the town of Melk and it's abbey, and the town of Dürnstein on the Danube. You can either train or take a ferry from Vienna.

We are considering the eastern europe rail pass.

That is a rip-off and waste of money. You can book all train tickets online, special bargains are available.