I think the store can deny entry to anyone for any reason. Mind you, some reasons (say, because they think she’s ugly) may not go over well with the clientele, but that’s the risk that the store takes. However, I think as an employee, it’s not your place to make a judgement call, especially if her actions are just annoying and not dangerous. While you are awaiting an answer, I think that this is a question for your manager. What does he/she want you to do?
Personally, I would need to know what she’s doing. If she wanted to come in and stare at me and do stupid gestures… so be it. It’s immature and she’s probably just trying to get a rise out of me. I would ignore it in the hopes that she would get bored. I would probably escalate things when she becomes bothersome to customers.