Dinosaur exhibition at the NHM, which isn't very far away? Not sure that it fits the 'active things' part perfectly, but the walk through the tunnel from the main South Ken tube station helps burn a little energy. There is also and opt-out route if you think walking through the room with the T-rex animatronic might be too scary/noisy/overstimulating, but personally I found the crowding more overstimulating (that was on a Sunday though, would expect it to be calmer in the week).

Science Museum is also nearby, but that felt distinctly less exciting recently than when I was a kid.

Transport Museum sounds nerdy as hell but is continually reviewed as being much more interesting and fun than people expect. That's a bit more central though and probably involves more crowded transport to get there, so depends if their neurodiversity gels ok with that kind of thing. Would recommend always traveling in the end carriage on the tube to reduce this potential issue, and finding a route avoiding covent garden tube station, where the exit is via quite large lifts, which can be quite overwhelming and crowded.

There's also the big Diana Memorial Playground in Kensington Park, but I think currently being renovated so might whether it's open may depend on your travel dates.