His mental state is one in which I legitimately think he could be dead any day (he has threatened suicide and seemed suicidal often and is doing some things now that make me think he is cycling and not doing well emotionally) - so I think I just want to see that he is alive?
I don't want this to sound harsh, but it is not your job to determine if he is alive or not. If he is actively making threats of self harm, or you are genuinely concerned because you haven't heard from him for a while and he has missed visitation with the kids (once the visitation schedule is in place), then you call the police and ask them to make a welfare check. It will either stop his hollow threats that are intended to manipulate you, or he will get the help he needs.
My ex made numerous threats of suicide. It was for the sole purpose of trying to manipulate me. I got tired of hearing it and I told him I would call the police if he ever said it to me again. Magically, I have not heard such a threat since.
You cannot let your concern for your STBX run your life.
Since he hadn't said any specific threats, it was more just that I could see his behavior escalating and it felt like he was capable of anything.
Document, document, and document some more. Be prepared, but again, don't let it rule your life. Keep a can of wasp spray handy (shoots 20 feet, aim for eyes).
A couple of weeks ago he was horrible to be on the phone and I told him that he wasn't allowed to treat me like that. Then he didn't call for text for two weeks - so I feel like its not my job to ask him if he wants to see them or not?
No, it is not your job to ask him. Make sure you put in specific days/times for his visitation and add a clause that he needs to give XXX notice if plans to actually see them, and if he doesn't show he forfeits the time (i.e., doesn't get "make up" time later). He has a history of NOT seeing his kids, so in this case it would make sense for him to give notification if he plans to to so. Also, if he is XXX late, he forfeits the time. You give him very specific parameters that HE has to follow (based on his pattern of behavior) and if he doesn't life goes on without him. This way, you do not need to remind him of anything or even ask if he is coming or not. It puts it squarely in his lap to act, or not.
I even talked to my therapist about what I would say to my kids if he did die.
If he dies by his own choices, THEN you deal with it.
I get it. I really do. My ex used the suicide threats for attention until I shut it down. He was also known to drive down my street during the middle of the night (he even admitted it to me). This is the same man that told me he could put a bullet in someone's head and not blink an eye or lose any sleep. He is also a firearms collector (and retired law enforcement), and was definitely had a mindset of the "if I can't have her, no one will." I put some security cameras up outside and he knows I am armed just as heavily as he is. I warned my XSO about him and didn't bring him to my house for a long time. Xhole didn't let up with his stealth stalker behavior until he latched onto a new victim (now wife). He now has someone else to focus his insanity on and leaves me alone.
The point is that I took precautions, but it did not rule my life. Nor did I constantly keep tabs on him to see what he was up to. I refused to give him that much power over me and my life.
If he is seen parked around your house, take pictures. Talk to your neighbors to keep an eye out as well. Try to keep any communication in written form (email/text) so you can have any escalations in writing. If he keeps up, you may get enough for a protection order. This is all stuff you can do without being so wrapped up in "checking on him."
As Trusted said, baby steps.