Definitely keep informing the police. If he does it again, notify them. Each instance will be documented, and there will come a time where he realizes the button doesn't work - he won't get you in person, he'll get the police each time (who will know how to respond if he is seriously suicidal), and they won't be really happy with his antics if he keeps faking.
Boundaries, boundaries, boundaries. Keep up the NC.
Furthermore, if you do involve the authorities/mental health professionals every single time he threatens, then, should he ever be successful, you will be able to truthfully assert that you did everything you possibly could to prevent it.
IF he continues to yell "sucicide" when he has the kids around: Seek a Court Order for "supervised visits only" stating: YOU DO NOT want your kids alone with him...because you don't want you kids to witness their father killing himself in front of them!!!
I can understand being alone; but I hate being with someone and feeling lonely.
Just how do I involve mental health services? I'm in the UK btw. I'm almost certain he has a personality disorder and needs help before he harms the kids, himself or me.
D-Day, June 10, 2012