IF there was no child--specifically, not  your child--then you would have the right to evict your girlfriend. You would have to do it properly, through the courts, if she didn't move out voluntarily when you asked her to do so, but it's still something you could do. (Note: if she's paying rent, then she's a tenant, not a guest; while you still can evict her, you would need to do so as evicting a tenant, which means at the end of the lease term, if there's a written lease, or after proper 30-day notice if an oral lease.)However, your child greatly complicates matters, since parents have obligations for the care of their children--a parent cannnot simply put a child out on the street. You need to stop thinking of this as primarily a landlord-tenant matter and think of it as a family court matter; you should consult with a family law attorney to see what obligations--including child support--you are potentially responsible for, as well as your rights, if any, to evict the mother of your child while she has custody of the child.