Do you want to stay central? If so, then here is my suggestion.
Go to the NHM, but avoid all the crowds in the museum itself and go down to a place called "Investigate" which is in the basement. It is designed for children and is a room full of specimens with table for the children to examine them - with microscopes, computers, rulers, paper for recording etc.
Then go to the Science Museum next door, but again avoid the crowds by heading to one of the lesser known galleries on the upper floors. Launch pad is excellent for children, but will be packed. See how you feel by then, if you can face the crowds. They do hourly science shows in the launchpad in a small theatre room which are worth seeing.
Then, go across the road to the VandA. I don't know this museum as well, but they have lots of art trolleys for kids in the various galleries.
This way, you can sample the three big museums but in a less stressed way.
Do google the Grant Museum of Zoology and the Pterie Museum. Buth right near each other, very central, very small and lesser known museums - but very good.