Just wanted to - say - yes, I've been in the situation of being accused
of planning to kill my mother (and it is not true), during her psychosis, paranoia, delusions, hallucinations. After getting her friends involved, they convinced her to go to the hospital. She wouldn't listen to me or to her doctor. In hospital, they put her on antipsychotic medication. Kept her there for a month. Discharged her back home - within a week she was going through it all again.
I had to leave - because I feared for my own safety (her irrational thoughts, paranoia, themes of murder, accusations, etc).
At this point in time - it's been 2 years already - she still expresses more delusions, paranoia, etc.