Yeah - the moods continue. Right now I am trying to focus on me and less on him (his moods, his motivations etc). I understand him well enough to know that his moods are based on guilt (when he tries to be nice) or on trying to impose some punitive measure (when he doesn't get what he wants). I try not to worry about it now.
I had a great day yesterday. The girls and I went to visit a friend whose daughter is close to D13. We sat in the garden and there were a few children there. It was lovely to see D13 laughing and engaged. She even spoke to me a few times (not conversation but not rude either). H was supposed to come over at some point (it was father's day) and I messaged him in the morning to wish him a happy fathers day and to find out if/when he was going to visit the girls. I also thanked him for tidying up the garden the previous day. I got a thanks back and confirmation that he would be visiting the girls but not the time. This is a constant issue with us. He refuses to say what time he is visiting. I didn't react, but simply said (later in the day) a simple "We are going out at 3:30, happy to move around as I know girls would like to see you".
I know you can't nice them back. That is not what this is about. This (for me) is about maintaining a calm consistent demeanor in the face of his chaos. I cannot change things. If neither kindness or anger works, then I would like to (try) choose kindness.