She's a trespasser! However, you gave the cops a way out, and they took it. What? You think cops are there to help you? Bwa, ha ha ha.
They've really put your mother in a bind. I agree with whoever gave you advice. You can't evict a trespasser. You can only evict tenants. The cops have decided she's tenant. The courts are going to think she's a trespasser.
You could put her out and change the locks, but if she calls the cops, they’re going to let her back in. Evicting her, therefore, is the only recourse you have available to you. Let's hope it works.
PS> Yeah, I think cops suck.