I have 11-year-old twin daughters. This summer one of the girls stopped wanting to stay overnight anywhere. This has never been a problem in the past. Now she won't even stay at her grandmother's house. She says she gets homesick. Is this normal to start at this age?
This abrupt change would be a red flag that your daughter experienced something that frightened her at her grandmother's. It may be something she saw, she did, she heard, or that was done to her. Try gentle and subtle questioning to see if you can get her to talk about her last visit to her grandmother's. Whether what happened was a real threat to her, or just how she perceived the situation, she needs help. Really listen to what she says and see if you can lead her to the point of confiding her fears to you.
You might also talk with her sister and the grandmother -- again in an off-hand manner. I suggest that you not reveal why you are asking questions up front. You also might want to consider whether anything happened to you -- were you in any danger, were you sad -- while she was away. She may be afraid of losing you or be afraid for you.
After you find what is frightening her, you will know how to proceed. If unsure, consult with a pediatrician or a licensed professional counselor.