Start eviction proceedings immediately!
Your mother could also try calling the police herself at a different time of day than they came before (so she won't inadvertantly get the same officers) and say, "there's someone trespassing on my property who won't leave." Only refer to her as a trespasser. Don't say she was [u]living[u] there, or staying there. Say that she was visiting and now she won't leave. The power of suggestion can be a powerful thing.
Also check your state's property code. Check in the first post in this forum to see if it has the info you need. See how the state defines tenant, tenancy, etc. If you find things that make a case in your favor have those laws printed out to show to the police when they come if they try to say she has to be evicted.
Karla in TX