If a new member is going to be destructive to a chapter, I think that it is a valid reason to depledge them. If someone is so troublesome, I suggest you contact your advisor and Headquarters immediately.
Back to the topic at hand, I am not sure of how this new member was rude to one of your initiated sisters. If she asked about not going to the second floor of a fraternity house, I think it is a legitimate question and an opportunity for the chapter to open a dialogue as ilovemyglo illustrated. If there is something more serious about her conduct, discuss it with the NM educator/trainer and her big sister. Good luck!
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