Activities for kids in Prague

Take a walk on the west side of the river down to Museum Kampa. You don't have to go in, but your children will like the penguins, and the big babies. It's a nice walk.

Another thing you should consider is keeping them up late one evening and walking around the castle and buildings on the hilltop at night. They are all lit up and look a lot different in the nighttime. There are not many people around after 9pm. Likewise one of my favorite memories is standing in the main town square around midnight with snow falling and all the pastel houses lit up. Beautiful.

Try https://www.praguegolfandgames.com/prague-things-to-do which is black light minigolf. 2+2 family ticket for CZK500 and other things to do. Good fun and a good "poor weather" option. Or there's the Karel Zeman Museum https://www.muzeumkarlazemana.cz which is all about the early days of film special effects (website in Czech but there are English reviews on the web) and that's CZK490 for 2+2 at the door or you get 10% off if you book online. Interactive, good pics for parents and kids can touch stuff as well...........

There are not many people around after 9pm.

That's not been my experience. When I first went around 20 years ago I recall the evening being busy and when I returned this October it was even busier and there were still crowds even at 11:30 pm.

The Royal Road, including Charles Bridge, is busy most of the day and evening and this is because of the narrow streets. Moving between the Old Town Square and Wenceslas Square is always busy. At the castle its really busy in the morning but the traffic really drops off after 4pm because all guides, and most tourists, know that last entry into the historic buildings is 4-40pm but the castle complex opens until 10pm so kids like the "scary picture" when they stand on the cathedral up-lights after-dark. If there's an event sports/market on the Old Town Square it will be busy. If not then none of the squares are really busy but the streets leading to them will be, especially 7-9pm when people are moving between restaurants and bars etc.
One other place for kids, on the Lesser Town side look for Malostranska Pivnice, walk down the road and turn right. That takes you down to the riverside where you can feed swans if you want or get there at dusk with some carrots and you may see Nutria (friendly animal that looks like a cross between an otter and a beaver).

If your kids are interested in things like trains, planes, cars etc, there is a big museum full of them near Letna park called the National Technical Museum. It's on several floors and is so big you could easily spend half a day in there. It includes many other interactive science based exhibits like computers and technology. I recall they had a whole TV studio in there.
There is also a Museum of Public Transport open on the weekends run by the Prague transport company. It's only a couple of euros entry fee and they have quite a lot of old trams and buses on display.
You could take them up to the mini Eiffel tower on Petrin hill. There is funicular railway to the top of the hill which is included in any day ticket for the public transport. Then there is a climb up the tower (or a lift) where there are some 360 degree views of the city.
There is a local photographer who does tourist photos, or you could check the internet for others.
There is plenty to see and do in Prague.

Just to note that the Funicular closes for maintenance in March. Last year 2018 it was from 5th March until 23rd March. Check the www.dpp.cz website (under fun and leisure) closer to your visit for the exact dates. You can still walk up the path from the lower funicular area.