How much help you will receive from the authorities varies from state to state and often, county to county within the states. Your local NAMI organization (if you have one where you are) can sometimes be helpful in letting you know what resources are available in your area.
At treatmentcenteradvocacycenter.org the state map will show you the laws for your particular state.
Threatening to kill someone will usually get a 3 day hold in a psych treatment facility. Is that how he was hospitalized before?
When it comes to making a diagnosis, the doctors and Social Security want to see proof that the situation has been ongoing for a long time and the psychosis is severely debilitating. You haven’t mentioned if he hears voices - the hallmark of schizophrenia, when he talks to himself is he talking to someone? My son had a long history of failed employment - did you get those details in the turnover from your ex? Disability is about being unable to work.
In my area, if my son had ever verbally threatened to hurt us or himself, the sheriff would have held him in a separate cell while waiting for an interview with the agency in Texas which has proven themselves to be nearly totally uninterested in helping our family members with smi - Texana. If the rep from Texana found them to be a threat to themselves or others - which the deputy says it means they have to say it to the Texana people, THEN they would hold them for 3 days in a psych treatment facility. To stay another two weeks, the person with smi would have to agree to further treatment. IF they don’t repeat it to the Texana rep, they just let them go back home to you. We had a camera that recorded sound outside our home. We wanted to be able to offer proof if it ever happened.
You can see how many of our family members with smi end up in jail. Some people will use jail and time in court before a judge as an opportunity to get a judge to order treatment. Court ordered treatments vary, in some areas it is done as an out patient. If they don’t show up for their shot, the judge can order them back to jail. For our family members with anosognosia, Dr Amador really recommends monthly injections.
I am not in the kick them out club, I am more into the help them find a way forward club. Clearly they do need help finding their way forward and figuring out a living/life situation that works. Having said that, my husband, who is my son’s father, was promised by me that if my son became an actual threat, he would have to live somewhere else.
When I built the guesthouse to get them apart from each other, both objected. My husband could not “do” LEAP for 10 seconds, he would get too excited when my son was in an episode. I held my ground and told both of them, when its completed ONE OF US is moving out there. A sense of humor helps, but seriously, I would have moved out there in a heartbeat 
Some people have their family members who are struggling with smi in campers and recreational vehicles, some are in guesthouses, some are in rental houses their families own or regular rental homes and apartments and some live very well with family members.
In my son’s case, he did know what would work for him - it did take him some down time without the pressure of supporting himself, to learn to adjust to living with his scz. I hope that someday he will take AP meds (anti-psychotic) in the meantime we just keep working LEAP to keep those lines of communication open.
His family had a crises team intervention and that’s how he ended up in the hospital.