These are great rec's here! I'm adding TOMORROW WHEN THE WAR BEGAN by John Marsden. It's about a group of teens who escape capture when Australia is invaded (fictional invasion set in modern times). They use guerilla fighting tactics to try to stop the people who've invaded their town. It's a little slow start, but definitely a page-turner once you get into it.
(Note: It's the first book in a series, but it can be read as a standalone. There is some sex in some of the later books that's probably too much for a 10-year-old, but the romance in this first book is less than there is in HG.)
I second the Shadow Children series, and I think that RUNNING OUT OF TIME is another great Margaret Peterson Haddix book she might like. It's about a girl living in the 1840s...who learns that she is not actually living in the 1840s, but in a historical replica village that's a tourist attraction in 1996. She finds out because there's an epidemic of illness in the village, and the people who run the tourist attraction won't give them modern medicine or let anyone leave and go back out into the modern world (there's a sort of sinister, dystopian feel to this aspect of it). So the girl has to escape from the sealed-off village into the and get help for her sick family. (And she has NO idea how to navigate the modern world - since she's never seen cars, computers, modern cities, etc.)