Let it go.
You are simply not equipped to deal with this. Even if you had no family to protect, there would be no benefit to your friend in exposing yourself to her irrationality. The professionals have a bad enough track record. There is no way you can have a better one. The cure rate for psychotic disorders remains around 10%, where it has been for many decades.
The problem here is that the government decided some decades ago that these pitiful people were better off in society than in institutions. This was no doubt true in some individual situations, and of course it reduced taxpayer costs, but the result is that there are MANY people out there who have no ability to function in society. People interested in our homeless situation soon discover that this is often the core problem for them.