I’d recommend for your daughter “The Art of War” by Sun Tzu and “The Prince” by Niccolò Machiavelli. And maybe a collection of family recipes of the Borgias. 
You could also try the His Dark Materials series by Philip Pullman.
The Melendy books (starting with The Saturdays) by Elizabeth Enright.
Savvy and its sequel Scumble, by Ingrid Law. They’re about an extended family where you get a superpower (but no control over it) on your thirteenth birthday.
Diane Duane’s Young Wizards series, starting with So You Want To Be A Wizard. Nine books in the series at present, and all of them wonderful. Strong female protagonist, and as the books progress you can see her growing up.
There’s a recent revision of all the books – so far only available in ebook format – that brings them up to date in a common timeframe (since the earlier books were written thirty years ago).
– Oh, and another vote for anything by Diana Wynne Jones.
May not be at all what you’re looking for, but my first thought for a subversive princess story was the webcomic Princess Princess (NOT Mikiyo Tsuda’s, but Strangely Katie’s). (Also on dA here.) I don’t know if it’s really for your 10-year-old, but you may be the best judge of that.
I don’t think she has any plans to release it in hard copy. I think The Girl from Hell City will come out in hard copy eventually, but she’s only one chapter in.
Huh. It occurs to me that outside the context of sites like Tumblr and Dreamwidth, Strangely Katie is a really odd name.
Probably out of print, but if you run across it, Thursday’s Child, by Noel Streatfeild is excellent. (Not one of her “Shoes” series.)
I’m in the middle of The Accidental Sorcerer, by K. E. Mills. So far, pretty good. There’s a princess in it, but she’s not a girly girl princess, she’s very practical.