I feel bad for you in this situation. You cut her off now, then you probably won't see your hat again.
Still be friends with her. Go to her home and hang out 'like good old friends'. And when she falls a sleep or even steps out to the restroom, search for your hat in her room, if you can't find it, grab something valuable and ran away of that house. Then you can give such item after she agrees to returns your hat.
She is a bully and she is testing your patience.
After you exchange items, then cut her off and put a restraining order against her. Also teld her you have gun at your home.
