Mary Poppins has had good reviews. But someone (a London cab driver in fact) told me the second half is bit 'long' for young ones so it would help to be familiar with the story first.
I loved Lion King but MP is obviously more Londony.
We're due to have an Indian Summer supposedly. It's still quite mild at the moment so don't go crazy on the thermals just think layers and waterproof options.
You won't be loud and American. Lots of Americans live here permanently. There are loud people everywhere!
As for sites to see:
Borough Market next to Southwark Cathedral for weekend food shopping (still probably won't get green top though)
Go to Fortnum and Masons, Selfridges, Harrods just to check out the Food Halls - so spectacular.
And in Fortnum and Masons go to one of the upper floors for your afternoon tea (St James tearoom - you can always get in unlike the Ritz and it's a proper English afternoon tea).
If your children don't mind a bit of walking I always had fantastic experiences doing these walking tours:http://www.walks.com/Homepage/default.aspx
(not Jack the Ripper which might be a bit much). You can quite often find a secret bit of London and a real flavour of history.
Walk along the South Bank (Westminster tube) and visit the Tate Modern and then walk over the Pedestrian Bridge to St Pauls Cathedral.
Museums - Natural History, Science for 'hands on' Launch Pad area, British Museum for Viking treasure and Egyptian mummies, Museum of London in the financial area the 'city of London'.
Walk around St James nr Green Park - check out Lock & co Hatters for a 17th Century shop front feel and the oldest barbers on the other side of the road (very Diagon Alley)
Portobello Market in Notting Hill
Take a boat trip from Westminster down to Greenwich for markets and national maritime museum.
Walk down Whitehall and marvel at the titchiness of our equivalent of the White House (10 Downing Street), wave at a Horse Guard and a quick trip into the Banqueting House where King Charles 1 was executed.
Chinatown behind Leicester Square for Dim Sum.
Princess Diana Memorial Playground (Peter Pan theme, brilliantly designed) in Kensington Gardens on a sunnier day.
The Sir John Soane Museum - completely weird and unexpected.
Avoid Madame Tussauds waxworks and the London Aquarium (both overpriced)