Hello Solost. Happy to help if I can. Your H would no doubt have a major tantrum if he realised how predictably he is following a script, wouldn't he? We've all been more or less able to predict everything he's done.
He is not thinking of the DCs here; he is thinking of himself and the esteem in which he is held by them. Just like he wants to run away from his colleagues, he wants to run away from the contemptuous faces of his children. Remember, this man can't bear anyone to think him foolish or stupid...
Resist pressure from him most firmly and say if he doesn't tell them, you will. I should warn you, you might see some nasty and dirty tricks at that point, including financial threats, but ignore them. You've got that sols appt. and that knowledge will stand you in good stead.
Tell him that you are thinking only of the children. You have brought them up not to lie and deceive and yet you are doing this to them every time you tell them a lie about his whereabouts. You are not prepared to continue lying in the face of their increasing questions and distress. You have taken advice (don't have to say where from) and know that it is time to tell them the truth.
In terms of what they are told, I would make the distinction between the unconditional love we have for our children, with the conditional love we feel for our romantic partners. Don't tell lies. When communicating the message to them as a trio, the words need to be understood by the youngest, so the message needs to be that he met someone else earlier this year and left in August to live with her. Most of all, that this is the reason the marriage ended.
You might get accusations of lying to them all this time, especially from the oldest. Apologise sincerely but say that for a time, you hoped that Daddy's new relationship would fizzle out as you would have tried again, but it hasn't and you couldn't do that now. He will wince at that last bit, incidentally.
Say early on that she has no children, incidentally as this will relieve them of a worry that he is being Daddy to other children.
Welcome their questions and answer them truthfully. Yes, you feel angry and hurt. No, Daddy didn't set out to hurt them. Yes, at the moment Daddy prefers this woman to you. No, you don't know if she's a nice person as you haven't even met her. Yes, Daddy might change his mind about her, but that doesn't mean he can have you back because humans are not disposable.
I expect that once the story is out, he won't be able to get out of the door quick enough. There are some specific ways I can suggest dealing with the aftermath, but let's take this one step at a time.