Hi T! Congrats on passing your webcam encounter, too. You are amazingly strong and I'd love for you to feel confident enough to apply it in every area of your life.
The following is meant as constructive feedback for you:
You did a decent job on the phone with him. I think the piece that I'd change is your lack of recognition that he's trying to drag you into the same old "I'm not where you think I am" argument.
I loved the "not a hotel" piece, but I do wish it were an active declaration rather than a reactive/defensive statement when he's trying to drag you into an argument.
An active conversation coming from strength might look like "H, you've left. You don't want to be married anymore, and I'd like the childcare arrangement to start reflecting that. I'm not comfortable with you sleeping here since you left the marriage and I'm especially not okay with you arriving so late and treating it like a hotel. It's time to start thinking about you finding somewhere else to live and getting on a regular childcare schedule. I'd hope you'd find a place with enough bedrooms for the kids and a suitable environment for them. Until you can do that, how about we give you every Saturday with them and you can come and pick them up and take them out to do something, but they still sleep here until you've procured housing? I'm happy to write all of this down for your records."
And that would happen when there is no argument or tension happening.
But you've been avoiding that conversation and I don't know why. If I had to guess, it's because you're scared it will drive him further away. But, T, should you be trusting old fears and anxieties, or logic? Because logically, he's left the marriage already.
T, I'm a bit alarmed that you didn't see your old patterns creeping in on the phone call with H. First, why answer? Let it go to voicemail. If you had to talk to him, the minute he was trying to dredge up the same topic that were part of your marital arguments, you should have said "I'm not interested, H. Where you spend your time is water under the bridge. Do what you want, my only concern is what directly impacts me, and that is your coming and going from the home."
Instead, we saw you take the bait because you so needed to launch the "I'm not stupid!" language at him.
T. Look at all that you have accomplished in your life. Of course you're not stupid. Why does it matter so much for you to be able to say that to him? Why is it necessary?
I wish you'd work to let that go. You still care so much what he thinks of you, and you are very wrapped up in him knowing that you know. From my recollection, that's already been established, and thus bringing it up again is nothing but pursuit, despite the fact that he's the one that called you. Because you were defensive and reacting to him. Giving him a reaction makes him feel powerful, and gives him the negative attention he's seeking from you.
Let him go. Drop the rope. Let him see, via your actions, that's what you're doing. You don't have to answer his calls. If he doesn't have the kids with him, there's obviously no emergency that needs your attention. And if you do end up in conversation with him, do not even entertain anything that has to do with the M, like where he's spending his time.
Here's what matters: He left. Now, living in that reality, what do YOU want? Because what you want matters. What he wants matters only a tiny bit, and it has to be about the kids.
I really want you to think about this. You've now given him more evidence that his coming and going bothers you, but that you're feeling too meek to do anything about it, so my prediction is that he escalates the outrageous comings and goings, since he knows it bothers you. You did not address his behavior from a place of strength and confidence where you are not afraid to actively advocate for yourself; you did it out of reactive defensiveness, and I anticipate he'll be trying to provoke an argument by doing what he knows bothers you.
It's getting to be way past time to address appropriate boundaries and formalizing a childcare schedule.
If you're worried about finances, he could pull them no matter what you do, and you've already delayed filing and pushed out that waiting period of 3-4 months.
The most powerful thing you could do for yourself is to stop worrying about what he thinks of you and what he might do, and become your own biggest fan and advocate for yourself. Also, formally protect yourself from what you know he's liable to do regarding finances.