Your plans are too ambitious. Don't underestimate travel times and physically moving around buses and trains and tube stations. London is not like Paris, Amsterdam, Barcelona, New York. The tube stations are well spread out.
Arrive at KX, check in, Holborn is Central Line for tube to Oxford Circus, so go to Regents Street and straight to Hamleys. You won't be able to get to Fortnums or Harrods, (traffic and tube disruption will be complete buzz kill for both of you). Also, neither will enchant a six year old.
You go for afternoon tea in Selfridges, on Oxford Street, off Regents Street, there is a smart restaurant that is surprisingly child friendly, but not condescending, near the deli but upstairs iirc. You should check TFL and catch the bus (as Oxford Street is bus/taxi only) as you've already done the tube.
Make your way back towards Holborn/ Waterloo, ( Bakerloo line Oxford Circus to Waterloo), catch the duck tour at the Millenium Eye / Waterloo Pier (get off at Waterloo and walk, tour PRE BOOK ESSENTIAL). Duck Tour includes a bus tour (bloody brilliant, lots of different routes) and an AMPHIBIOUS TRUCK on the Thames. Properly exciting.
Then either go on Millenium Eye and supper on Southbank (5 min walk from where you get off) then Northern line, change at Leicester Square for Holborn and bedtime.
Alternatively, if you can't get on the Eye, Northern Line 3 stops back to Leicester Square (Chinatown). Go for a wander. Eat anywhere except on Leicester Square in Chinatown.
Both are near your base for tired legs, bus/taxi or 2/3 stops on the tube, bedtime.
Day 2 Covent Garden Piazza, 1 stop Picadilly line. Have breakfast/brunch in cafe. In the piazza jugglers, clowns, those creepy people who spray themselves silver and move once an hour, that will entertain but CRUCIALLY are very close to walk to your theatre matinee. Go to matinee. Look for pre/ post theatre meal deals.
If you missed Chinatown previously go there after your matinee. Or eat on a meal deal
Day 3 pack up, down to Waterloo Pier, 4 stops. You catch the catamaran/river ferry ( very sleek and exciting) to Borough Market, so both boat and food. You can mooch around, eat, relax. Borough is on the Northern line directly , so then the six stops back on Northern line to KX.
Everyone's happy. I missed a career as a tour guide clearly
Have a brilliant time, London, my favourite city.