I know you're in such an awful situation. I'm thinking of you and your family.
I'm not a mental health provider by any means. But my H does some work in veteran suicide prevention and I'll share some ideas that you can take or leave (a colleague of mine's H was saying some suicidal things and my H gave me the following to share with her):
-- my understanding is that you are supposed to take any sort of suicidal comment seriously.
-- if you can access a suicide prevention hotline where you are, call it. It is not just for the person at risk-- they can help you to identify risk factors and what to do.
-- you might still take the appt you made for your H with the psychiatrist (if he doesn't) and explain what is going on and get some professional advice. For instance, I wonder if getting his family involved if alienated is a good or bad thing... my instinct would be good, as long as they can put their own emotions aside to support him... but I also know that there might be other things at play that would in fact make it worse.
-- does he have a firearm in his house? You might just ask him. My understanding is that is a significant risk factor.
Maybe others on this board have more knowledge and can chime in here. If it were me, I think I would check on him, though maybe calling isn't the best. if you know where he is maybe you can leave the kids with someone and go to see him and talk. It was good that he opened the door with calling the other night and good that he sees you as someone he can reach out to.... maybe you just follow up on that thread, nothing to do with your R or the kids or any logistical stuff that you are usually communicating with him about, just... you're here for him, you care about him, you can listen and then encourage him to go get help.
I think you can still care about him and not let his actions affect you... when reading your last post it feels like you ARE detached, you didn't let the sex thing throw you, you didn't let his bailing throw you, you didn't let his calling throw you. You were present and kind and calm. You have incredible emotional strength to get through all of that in the way that you did. I would guess you have the strength to reach out to him and help support him through this, if he allows it, without pushing you off your detachment path. (I do think you need to be there for yourself first (put the oxygen mask on yourself before helping others) but in your case I think your oxygen mask is already on.)
And of course you can totally leave all this armchair psychiatry behind-- just wanted to offer a few thoughts and to let you know I'm thinking of you. You are a strong and amazing woman and whatever happens you have been and continue to do the right thing.
Me (46) H (42) M:14 T:18, D9 & D11 4/19 - 12/19: series of escalating BDs 9/20 - present: R and piecing