The Torygraph has a nice article about QEII and MO.

[Captain Hilts]

http://www.telegraph.co.uk/news/worldnews/northamerica/usa/michelle-obama/5523623/The-Queen-and-Michelle-Obama-forge-firm-and-affectionate-friendship.html

Mrs Obama, and her daughters, Malia, and Sasha, were shown around the Queen's official London residence and its 40 acres of gardens on Wednesday – the final day of the family's sightseeing trip to the capital.

It was a birthday treat for Sasha Obama, who was eight on that day. It is understood they were warmly greeted by the Queen at the end of their hour-long visit.

...

It is the warmth of their new friendship that led to Mrs Obama contacting the Queen to inquire whether she would allow her daughters to see Buckingham Palace, which has been the official residence of the sovereign since the mid 19th century, when Queen Victoria was on the throne.