This man is not 'working on your relationship'. He is doing nothing to repair the damage and he is abusing you. Oh, and he's not sorry - he expects you to go back to normal every time after he has pressed the nuclear button.
Well OP, you will do well if you only stay in this marriage a year. And yes, next time he threatens divorce I would take him up on it. Although, as you say, he doesn't actually want to up and leave - no! he would want to make life as difficult as possible for you. Properly leaving and slamming the door behind him would be far too neat.
This used to happen to me with my EA XH. He would escalate the argument and finish it off with threatening divorce or saying 'let's split up then'. This was an effective way of getting me to back down. I would be virtually grovelling in despair to make it better. The start of the disagreement might be trivial - ludicrously trivial, like, how best to cook fishfingers - but it would end with him threatening divorce and me going 'No please don't say that!' and crying because it was so sodding hurtful.
That is exactly the effect your H wants to have, just as my XH did. Horrible, cruel and unforgiveable. He doesn't love you. I thought I could repair the marriage too. I was misguided. I thought he loved me, but it took a long time to realise (duh!) that someone who could treat me with such contempt had no love for me. He would also confuse me by sometimes saying he did love me, and then starve me of affection and any kindness.
You need to get your ducks in a row. This nasty man won't make it easy for you. Get support from your family - they obviously want you away from this man. And get the number of a good family lawyer - specifically ask if they have experience of abusive spouses.
If you need him to move out, I suspect he won't go if he thinks that you actually want him to go. So you need to be subtle. Perhaps he might 'decide' that he needs some space... let him go, agree reluctantly that he might be right etc.
You will be far better off without him. Have no doubt that he is horribly abusive and that you need to get you and your dcs out of his orbit. Good luck.