It’d help a lot if you gave your arrival time at KX and flight time from Heathrow the following day.
I agree with others that unless you have an early flight you’d be better staying in central London than Heathrow.
However, if you can’t change that I would do as others have suggested and leave bags at KX (left luggage service is available).
Depending how much time you have available I wouldn’t attempt all the things on your list. Exploring the Tower of London can take numerous hours as can the Nat Hist Museum.
If you aren’t familiar with London and want to see some sites and can handle a bit of walking, and the weather is OK what I would suggest is:
Drop bags at KX
Take piccadilly line to Green Park.
Walk through Green Park, see Buckingham Palace.
Through St James Park (look for pelicans) to Horse Guards Parade. Down Whitehall, past Downing St to parliament square. See houses of parliament/ Big Ben.
Get on an Uber Boat at Westminster pier down to Tower pier - you will see sites from river including London Eye south bank and the shard.
At Tower, rather than the Tower of London I would recommend Tower Bridge museum. You get to walk over the top section of Tower Bridge with a glass floor, and great views (if you are v lucky the bridge may open - you can check scheduled opening times online). From here you can see the Tower of London. It is v child friendly, allow 1-2 hours.
From Tower Bridge you can walk to Tower Hill tube and take the circle line back to KX to pick up your bags.