Two weeks Prague to Budapest with 2 kids

We're heading to Prague, leaving two weeks later from Budapest. In tow will be our two curious, outgoing, history-loving kids, 6&8 years old. Our noses have been stuck in tour books and we've got good ideas for exploring in Vienna and Budapest... But Prague is not exciting us. The astronomical clock and the mini-Eiffel tower and a tour of the castle in Prague seem to draw us, but otherwise I'm looking at a day in Kutna Hora and a couple in Cesky Kumlov. What am I missing in Prague? Surely if it was just adults my focus would be different and we'd be drawn to other things, what am I missing for exploring with the kids?

We're not focussed on touring the theme parks and playgrounds of the world, the kids are happy to learn about history and visit museums. One loves opera. One loves military history. (weird kids, I know!)

Is the Alchemy Museum in Kutna Hora open? I saw something that indicated it might be no longer open.

If we go to explore KutnaHora for a day, do we just take a bus/train out and back? or move lodgings for the night? is there public transport to Cesky Kumlov from Kutna Hora or would we need to return to Prague? Maybe with the four of us we're better off hiring a driver and car? Goodness who knew I had so many questions in me... I saw where train tix are 50% cost for kids, are bus tickets the same discount?

Any suggestions for lodging with kids in any of our locales? Some of the hostels have 4bed family rooms but a B&B/pension/apartment would be cozier if the price weren't too dear.

We're thinking 3-4 nights in Prague (including KutnaHora), 1-2 in Cesky Kumlov, 2-3 in Vienna, and 5-6 in Budapest.
We're happy for any/all suggestions for adventures with the kids in these and nearby locales!

Thanks LP/TT!