If you have a contract the landlord will have a difficult time evicting you for a personality conflict. However, if she wants you out and you want to leave, you have the ability to negotiate any resolution that you desire to let her out of her obligations under the contract.
If the contract is for a week to week, month to month tenancy, the landlord can give you notice under the agreement and force you to move at the end of the notice period. Obviously you can also be given notice if the tenancy is for a longer duration - but if it is a short tenancy the landlord can get you out much sooner by giving notice.
This information is provided for general informational purposes and is not intended as legal advice. An attorney licensed in your jurisdiction can answer questions specific to your specific fact situation and provide you appropriate advice as necessary based on the specific facts of your matter and the jurisdiction in which you reside. If you are in Arizona and interested in discussing your matter further I can be reached at: (480) 838-9000 Mark D. Fullerton, P.C. 1839 S. Alma School Road, Suite 275 Mesa, Arizona 85210