My neices behavior is worrying me. What's wrong?

If she's saying that she doesn't want to stay home, then something is happening at home that is terrifying her. It could be anything from nightmares about monsters to someone abusing her physically or ually. I'm not accusing anyone in your family of anything, I'm just offering possible scenarios. Keep trying to talk to her, and keep asking her why she doesn't want to stay home. If she continues to be upset, take her to a child therapist. They are trained to help children open up their feelings.