TFL guidance is to go through the wide gates. What you can do is partly informed by how much you want to spend eg the zoo and London Transport museum are payable, and their interest. My grandson loves the science museum with all its machinery but most kids of that age will get something out of it. If you go to Buck Palace then also go to St James Park - I was a metre away from a heron last week - and through to Trafalgar Square. I would second the Thames Clipper all the way to Greenwich from Embankment or Westminster via Big Ben (still in scaffolding), the London Eye, Tate Modern, the Shard, past the Tower and under Tower Bridge and finally the Cutty Sark. Have a break/ run around Greenwich Park and consider walking under the Thames through the tunnel to catch the Docklands railway. Try and sit at the front as there’s no driver!
If you only have two days then you need to make some choices which will also be informed by the weather. The Imperial War Museum is good but a bit more difficult to combine with other things. Enjoy!