Does the girlfriend have any rights?

She has rights. You have allowed your home to be her residence, and now you cannot just kick her out into the street. You have to evict her if she won't leave voluntarily. I am assuming you have a child with her, since you put this under the child custody heading rather than landlord tenant. As such, you really need to consider what you are doing, and how it will impact your child and your custody rights, before you proceed.

She does have rights, but they are rights extended by law, not contract. As a result, you need to merely meet the requirements of NRS 40 and 118A. Typically, this means she will have an assumed "month-to-month" tenancy, so she gets 30 days written notice. (You will probably want to mail that Certified/Receipt Requested or get her to sign a copy as having received it.) Bottom line, she does have rights, but you have remedies available to you.

Not just because she receives mail, but because she actually lived there. Rent or not the courts and the police will require an eviction.