Your days would be far too crammed packed for me, but I realize everyone is different and does things at their own pace. Some thoughts, though, for what they're worth:

Saturday- I agree with alanRow, pick up the book first as you've got it reserved. Arriving at your hotel at 3pm leaves only four hours before the bookshop closes. IMO that isn't much time to freshen up and putter around your hotel room, take a bus tour, eat dinner, AND browse the shop before it closes. I would buy your book first, then play the rest of the evening by ear.

Sunday: I would recommend eating lunch at the Tower. The food and the price are surprisingly decent. So 9-12noon easily covers the Tower, let's say 1pm to include lunch. That gives you 5 1/2 hrs before LLL begins at 6:30pm, and you'll need to actually be there by 6pm, I would think.

Wouldn't you want to leave sone time to go back to your hotel to freshen up before the show at the Globe? Maybe eat a high protein snack in your room.

I'm just not sure an hour at West. Abbey and 2 hrs in the Cabinet War Rooms are possible to squeeze in between an entire morning at the Tower and a 3 hr show at the Globe. At least without dying of hunger and exhaustion in the middle of LLL.

I would prioritize, so if you're tired or pressed for time you know ahead of time what to skip.

Monday: You may want to consider eating lunch in St James park after your Buck House tour, if the weather is nice. You can grab a hotdog and a drink at a kiosk.

IMO fitting in *both* the Museum and Library before Wicked is too much, unless you are okay with very quick visits. I'm with noe847, the BL is one of my favourite places, I could happily spend all day. And the BM is something to behold.

I would be inclined to skip the tour of Buck House and fit in longer visits to the BM and the BL instead. The Fancy That shop across from the Musuem is also quite fun to browse and shop for cheap souvenires. But if Buck House is a must-do, then I would prioritize between BM and BL.

Have a great trip, sounds like fun exploring London with your daughter. Whatever you end up seeing and doing, you are sure to have a wonderful time

One teensy item: If you land by 1:20 you are wizards if you make it to your hotel at County hall anywhere near 3 p.m. Heck, you could still be walking to arrivals from the gate at 2:00. Landing is not in the terminal w/ your luggage. 1:20 is out on the tarmac where you may even have to wait for a gate.

So I would consider myself lucky to be at County Hall by 4:00. By the time you check in and get organized, you won't have much time for any touring/bus riding before getting to Hatchard's.

Customs and travel to the hotel could take much longer than you expect.

For the Shakespeare, I would pick up a copy of the Cliff Notes of the Play and also a copy of the play itself and work through a bit of it with her. If she knows the general plot line it will go better for her. The first time my mom took us to a Shakespeare Festival we all read the play aloud. Great memories.

I also would encourage visiting the train station that appeared in the Harry Potter movie. (Was it Charing Cross?) I have never been inside Buckingham so can't address that.
But that would be instinctively what I'd miss.

>>I also would encourage visiting the train station that appeared in the Harry Potter movie. (Was it Charing Cross?)<<

King's Cross, where you can take her picture trying to push the trolley through the wall at Platform 9 3/4.

Kellye, I admire your self-control! My daughter will pick up her copy at midnight, but she has to work the next day - I have definite plans for her book... :-D She is going as Professor Trelawney and her friend is going as Luna Lovegood.

Lee Ann