AIO for trying to put my mother in a full time nursing facility

My (36m) mother (59f) has several mental disorders including Schizo Affective Disorder(bi-polar type), CPTSD, Generalized Anxiety Disorder, ect... She has already been hospitalized 4 times this year for mental health and attempted self deletion and has been hospitalized no less than 100 times in the past ten years. My step dad (54m) is the strongest, calmest, most selfless man I have ever met, they have been together for 25 years and this man has sacrificed everything for her up to and including his own physical and mental health.

Now to the dilemma, this last weekend she attempted again and my step dad called me completely breaking down, just utterly sobbing(this man rarely cries) that he is so scared, he's broken, he doesn't know what to do anymore, and how he is trying so hard to keep her safe and take care of her but he just can't be there all the time. So I finally had enough, I told both him and my mother that she needs to be put in a full time care home where she will have the round the clock care and supervision that she needs. Now she is lashing out at the entire family saying that we are throwing her away (not true the facility is literally a 7 minute drive from my home), that she will never see us( again it's a 7 minute drive), that we must hate her (because apparently not wanting her to die means we hate her), ect...

I know I'm doing the right thing but all of her vitriol is getting to me so I figured I'd ask y'all AIO???