Unfortunately if you create a landlord/tenant situation (money need not be paid) you have to go through legal means to get people out. It is never a good idea to issue an open ended invitation for people to stay in your home.
Neighbor wants the guy out, but since she lets her worthless son live in the house, and the guy was invited by the son, it's debatable what recourse she would have. She's already suffered a heart attack due to the stress caused by the son.