Hi. I actually made an account so I could respond to your post :)
I went to London 3 years ago with my husband. I loved it so much I'm going back this fall with my 13 & 9 year old sons.
I think you're planning too much in your days. This is what we did...
Day 1: arrived 1:10. Got to the hotel after 3pm. Went walking, dinner, crashed.
Day 2:
British Museum at 10:00 (loved, the kids will love, spent several hours there & ate lunch in their cafeteria),
British Library (there's a copy of the Magna Carta there, plus lots of old books and documents, including Queen Elizabeth I. We loved. I'm taking the boys. King's Cross Station is close by (Harry Potter), which we didn't see before, but I will take boys this trip),
4:24 train out of Watford Junction to Harry Pottery studios. Looked at EVERYTHING, and still were done before close. Definitely going again. Got back to London around 10pm.
Day 3:
Mind the Gap Bike Tour to Windsor. Loved Windsor, liked the bike tour, took up the whole day.
Fell asleep in the play we went to that night :) (Would pick Hampton Court Palace over Windsor with the kids if you have to pick one.)
Day 4:
This day was too busy. We both wish we'd had time at all three things.
9:00 on the dot at the Tower of London. We were there for hours, with no lines, and still didn't see everything. The kids will love it.
1:00ish??? at St. Paul's Cathedral. Beautiful, but I think the kids will like Westminster Abbey more if you have to pick. Knew we had to get to Churchill Museum, so we didn't wait in the (fairly long) line to get to the tip top. We did eat in their basement cafeteria, and it was very good. On the backside of the altar, there is a large book containing the names of every American soldier who died during WWII (or D-Day, can't remember). It was very moving - the British have not forgotten the sacrifice.
3:30 Churchill Museum. We loved it (ok, we loved everything) and were the last ones out.
Saw a musical that night.
Day 5:
Took the train out to Hampton Court Palace. LOVED. Many times we commented that the kids would like this, or that.
Working kitchen that makes food Henry VIII would have eaten, big maze, largest grape vine in the world, etc.
We stayed from open until 3:1ish.
Did more wandering (we'd been wandering a bit the other days, too)
Decided we were too exhausted to go the Globe Theater that night. Regret that decision, but we were tired!
Day 6:
9:30 Westminster Abbey, which is beautiful. Lots of statues to look at. Just happened to be in the right spot at the right time, but got to go up the stairs, behind the altar, to a brief prayer service. This is the area where the brides/grooms go during royal weddings to sign papers or something, as well as being the destination for centuries of pilgrims. Cool.
1:00 Almost missed our reservation to Buckingham Palace. Loved the exhibit about the Queens coronation. The exhibit was one of my favorite parts of the trip, but I'm not sure I'd take the kids to the palace.
In the nick of time to see the Mews. Cars, Carriages, Horses, including the gold coronation coach.
5:00ish went to Evensong at Westminster Abbey. Cool experience, not doing it again.
We then left London, went to Salisbury (Stonehenge, Cathedral, Old Sarum), took a train to Portsmouth and took an overnight ship to France, where we spent the day visiting the D-Day sights.
Point of all this....I think we saw 3 things a day and felt rushed. I really think you will regret Day 2, because you will barely see anything at any of the places you go.
Enjoy!