Berliner Unterwelten is my number 1 recommendation for Berlin. Not sure if your children will be old enough (in actual age or maturity etc.) but its worth checking out the website – https://www.berliner-unterwelten.de/en/index.html
Its nice to go down to the Wansee and go on a boat trip (easy to get to on the S-Bahn), and Potsdam just beyond is a nice town but not so much for children there.
The former Templehof airport is good and a bit of a more open area for a run about. We’ve hired scooters in he past and whizzed about there.
Going to the Teufelsberg could also be good with children – lots to see there.
Also ‘Gardens of the World’ and the cable car at Kienberg.
If you wanted a trip further out of the city, Tropical Islands is an indoor water park in a former airship hangar which I believe is the largest free standing hall in the world