The relationship has taken its toll and life has become miserable between us. Chalk up to irreconcilible differences but I want her to move out so I can find peace in my life again. She has a daughter living with us as well. What is the Law on such a case? Do I have to give her ample notice or can I remove her from the apartment immediately?

You evict her as a tenant unless she's also on the lease.

If she is not on the lease, here is the law: General Eviction Information | Legal Assistance of Western N

Judy is correct but we could use more datails. Did you ask her to leave yet, start by doing that, if she says NO then you can take steps to evict her. Has she contributed toward the rent?