I almost positive she smokes in the apartment and she is breaching the lease by doing so, however, this is obviously too difficult to prove.
I concur with Mr. Schutz, but I'm curious as to why you believe her smoking in the unit would be "too difficult" to prove. As the landlord, you should have (a) reserved the right to enter to inspect the unit for breach conditions and (b) probably smell cigarette smoke outside, regardless. Your own testimony of what you've experienced would be competent, probative evidence that your tenant is breaching the lease by smoking indoors. You don't need to recover physical evidence, or catch her red-handed.
The foregoing is not legal advice, and nothing in the foregoing shall be deemed to create an attorney client relationship. If you feel you need to speak with an attorney regarding your issue, it is recommended that you contact an attorney with expertise in your area of inquiry. The information related above is purely for informational purposes, and should not be acted upon without speaking with qualified counsel familiar with you specific situation and the laws related thereto.
Landlord / Tenant Lawyer
If the building is a two family owner occupied building, you can get rid of her for any reason. However you may have to wait until the lease expires and give appropriate notice.
Administrative Law Lawyer
You could send the tenant a Notice to Ceases (that the Tenant is in breach of the lease) or a Notice to Quit (that you want the tenant to vacate at the end of lease) If the tenant is month to month you can server a 30 day notice at the begining of the month.