Visiting the theatre is cathartic, and avoiding all mentions of mothers and daughters could be impossible. However, I could see where shows like Grey Gardens, Mamma Mia!, and Hairspray wouldn't be the best of choices because of the strong mother/daughter themes.
Something like Rent or Chorus Line might be shows that she could relate to right now even if they have themes that might hit close to home.
If you do want completely cheerful, I agree that Spamalot is a great deal of fun.
The Apple Tree does have a sad ending to Act 1 (private message me if you would like details), but in general, it is a really fun show with lots of humor. Kristin Chenoweth is amazing in it, and she is generally a hit with most 11 year olds!
I wouldn't suggest Spring Awakening as I believe that 11 really is too young for this show. There is nudity and many serious subjects.
Ask her what she would like to see. I bet she will have some opinions. If she would like to see Company, I'd say go for it!
So, that was the Drowsy Chaperone. Oh, I love it so much. I know it's not a perfect show...but it does what a musical is supposed to do. It takes you to another world, and it gives you a little tune to carry with you in your head for when you're feeling blue. Ya know?