Well, that all depends...is she a co-tenant on the lease? If so, no, she has just as much right to be there as you do. Is she a co-tenant, pays rent, etc. but just is not listed on the lease or only listed as a permissible occupant rather than a signer? Less clear, but without good legal cause you are likely to have resistance. Is she just a guest who has now over stayed her welcome? Yes, you can get rid of her but if she refuses to voluntarily leave, you must go through the court process to get rid of her - properly drafted and properly served notice and time to vacate; file suit if she does not vacate; obtain a court judgment kicking her out; and then, if she does not get out in a timely manner, have the Sheriff come remove her from the property. All in all, it can be both expensive and potentially time consuming depending upon your local court's procedures and administration. IF you decide you need to go through the legal process, you are strongly advised to consult a local landlord-tenant attorney for help - the process is highly technical and unforgiving. The slightest mistake during the whole process - in either substance or procedure - can result in your losing, owing her court costs and possibly attorneys fees, and you have to start over, that much further down the road.
All that said, much better all the way around if you can calmly and rationally sit down and talk with her, telling her things are not working out and it is better for both of you for her to move out. You may want to even offer to help, either physically and/or financially, if it will get her out now. Trust me, if you think she is a pain now, just wait until you file suit against her in court and have to come home to sharing the same apartment that night...and if you screw something up and she wins, forcing you to start over and keeping her there for at least several more weeks, things are likely to turn downright ugly. A negotiated agreement here is a far better outcome - faster, cheaper (even if you have to pay her to move), far less aggravating, and might allow for some sort of continuation of family relations albeit perhaps a bit down the road. Good luck.
Nothing contained herein should be considered as legal advice for any specific situation and nothing herein is intended to create a lawyer-client relationship. Every case is very "fact-specific" and persons wishing legal advice on a specific matter should contact me or another attorney for an appointment to review their particular circumstances and to create a lawyer-client relationship. Gregory L. Abbott, Attorney at Law, 6635 North Baltimore, Suite 254, Portland, Oregon 97203. Tel: 503-283-4568; Fax: 503-283-4586; Email: email@example.com. Specializing in Consumer and Small Business Law.