Hello again, Pepita. You have a good list, I've done most of them across 11 Wimbledons. The main things you don't have (and you have two small kids, right?) are Windsor Castle and Stonehenge, which you can do (along with Bath) on a nice day trip via Evan Evans Tours, as I did once. All 3 stops are good for kids. You also might consider another E-E trip I've done: Wawrick Castle, Shakespeare's home in Stratford-on-Avon and Oxford.
As for art....You have Tate Britain...I assume for your kids one art museum suffices, and you chose it over the National Gallery, National Portrait Gallery or Tate Modern. All four have their fans. Haven't been to the two Tates, yet, but I'd think National Gallery has the best collection of notable works.
Just be sure you are at Buckingham Palace for the Changing of the Guards...you should get their in enough time to stake out a good spot. And your walk around Kensington Gardens needs to include going by Prince Albert Hall, with the Prince Albert Memorial across the street. Gorgeous.
My main suggestion for the other two days to fill was already mentioned -- a day trip to Greenwich via a river cruise. The buildings are gorgeous, the maritime museum very kid-friendly, the view from the top of the hill is the best, and be sure be spend plenty of time in the market.
And maybe it's not kid-friendly, but if it interests you, do the Fullers Brewery Tour. Is fun, and there's free samples!