Prisons for mentally ill commiting crimes?

I find (where i live anyways) to have too much lenience towards mentally ill and prison time, and tend to favour the mentally ill over the safety of people

Heres my example

My grandfather has a restraining order against his daughter (my mother) for his own safety, sge has put him in the hospital 5 times and drained his bank accounts at least a dozen. On saturday my mother decided to hunt him down for money and chased him around for 2 hours before he was able to get help. He called me and i went to go pick him up from the police station and what do you know shes standing right outside the station waiting for him so i tried talking to her and she assaulted me and ran away. Monday she turned herself in for her warrant knowing they wouldnt keep her long. Today (Wednesday) she was released. I called her probation officer and asked why, she responded and i quote "her mental illness prevents her from understanding punishment"

What should happen with people who are too mentally ill for prison but not sick enough for hospitalization? Like sure shes not a physical threat to the majority of society but she is a threat to my grandfathers safety, im not worried about myself as im trained to physically deal with her but im concerned about him when im not around