I think the fact that the Queen Mother was Scottish, and descended from Scots and Welsh royalty is interesting. As far as I can tell, Prince Charles would have very little Welsh in him (or no Welsh at all) had his grandmother not been Miss Bowes-Lyon. The fact that Elizabeth's family turned Strathmore into a hospital during World War I and hired nurses, while Elizabeth provided emotional support to soldiers is also fascinating. Strathmore got a reputation for being able to comfort and rehabilitate the soldiers with the worst shell shock, and Elizabeth was credited with much of that success. She kept in touch with some of the men for the rest of their lives. She turned her future husband down on his first two marriage proposals, but then accepted and went on to become the mother of Queen Elizabeth. Naturally, a teenager would probably like watching the movie The King's Speech after hearing about Elizabeth.
Helen Mirren's The Queen is another excellent bit of modern media that a teen or child might enjoy. The importance of horses to both Queen Elizabeth and her mother (they divided up their interests, I believe Queen Elizabeth took the "racehorse" bit and the Queen Mother took the "steeplechase" bit - someone correct me here if I've got it wrong...is interesting to a child (and of course watching the original National Velvet, while not about royalty, is still about a sport that royals and aristocrats still favor (along with polo), and Princess Anne is of course, an incredible horsewoman.
I think the fact that the Queen married for love and is still with her handsome prince is a lot of fun for a child (and there are youtube videos of her, much younger, introducing us to the Crown Jewels, and bits of news about her coronation and, I believe, her wedding).
And don't you think kids and teens would enjoy seeing pictures of Prince Charles and company in their kilts? Both of his parents have a bit of Scottish blood in them, and they are very proud of it (although the amount of geography a child or teen would learn just by looking at the immediate ancestry of Elizabeth and Philip is amazing: Elizabeth's great grandmother was a Danish princess; Prince Phillip's father was of course Prince of Greece and Denmark, his paternal grandfather was King of Greece, his great grandfather was King of Denmark, one of his great great grandfathers was Nicholas I, Tsar of all the Russias.
My kids still find it interesting (they are in their 20's) that Prince Phillip's great great grandmother was Queen Victoria - who is also Queen Elizabeth's great great grandmother. So that makes them third cousins, I believe (someone correct me here, again, if I am wrong).
That's what comes to mind, anyway. What a fun topic.