OP I see in your DH's responses and reactions many similarities to my own DH when I discovered his affair and we are still together, but it has been a long hard slog with many, many ups and downs. We are getting better though and I always think that Tessa's advice is so wise - it's not just whether you can forgive: it's whether if you can, or even if you can't (I can't but am learning to live with that and the visceral rage is diminishing but the pain gnaws although less frequently than it did), you are also able to live with this new version of you and he. So that means rebuilding from basics and it's desperately difficult, because you are having to do that whilst still enduring the ongoing pain.
I have to say that your DH did far better than mine in terms of his responses in that he has dumped the OW (I assume you are quite sure of that?), transparency with phone and emails etc. My DH put me and our DC through hell for some months when he vacillated over whether he could put his 'great love' aside and even when he claimed NC, he was still using a secret email account, the work email (he worked with her - fatal) and texting.
I won't bore you with how it all came to an end with her ultimately - but boy did with pay the price in terms of her subsequent rage and attempts to get 'revenge' on both him and me - but what I do know is that his talk of the money settlement etc is really an attempt to scare you to accept that he does want to make a go of it and not go down the route of divorce. Sadly, like my DH, his tantrums and sulks are all too indicative of the mememe response that so many men seem to indulge in when caught with their trousers down. My DH says now that much of his own petulance was (a) because he was still emotionally in the OW's camp and, frankly, didn't give a shit about my feelings (you become a non-person to your DH/DW when they are in the throes an affair), (b) he didn't really want his family life to end, established as it was over 15 years, but (c) he still wanted the excitement of the affair as he had become besotted with the OW, but knew that now they had been discovered, the 'party', the 'bubble-world', had gone for ever, and he now had to deal with real life shit rather than never-never land. It didn't help that his OW was determined that the affair would NOT end and had made it quite clear to her DH that she was 'off' as soon as my DH turned up with his white charger.
The months - nearly three years actually - I have endured of this massive grenade in our marriage have been agonising but I was never in the LTB camp. My reactions, the shouting and striking him, were the same as yours and I make no apology for them. He is a big man and I am a small woman (I know that doesn't make violence right, btw) but my incomprehension, devastation and shock were so great that, yes, I hit him very very hard across the face on first discovery, and then once again when I discovered, several weeks later that his lies about it 'only' being a EA were just that, lies, when he was compelled to tell me about their numerous sexual liaisons, including in my own home, because she had threatened to tell me (in a bid to get him to leave me and go to her).
Subsequently we have had 'honeymoon' periods of happiness, deep lows - usually caused by my hurt bubbling over and overwhelming me - and lots of conversations about divorce. It is always me that says I can't do this' and talk of divorce - when he is driven to the limits of his ability to cope with my anger, he says 'OK - have your divorce'. But thirty minutes later we are now able to make up - a year ago our row would rage for hours, with mutual storming off (but always returning after a drive round the block because although living with each other was so, so hard, being apart was even worse).
I have no illusions though that if his remorse wasn't absolute and genuine, which it is, and if he didn't suffer such obvious mortification and feel such a total fool for his behaviour during the affair and in the months after discovery, I would NOT be here still. But I am only at that stage now - at the point that you are, I could not even begin to contemplate a life without him, which is why I fought so hard for our marriage. All my friends at the time, bar one, said I should throw him out. But that wasn't the right route for ME.
In retrospect, because he was still so besotted with the OW, he feels that mine was the right choice and he knows how hard it was for me, particularly as his behaviour towards me was nothing short of callous and wicked. Reading that he would rather have had his children with the OW (in one of the many emails from him to her that she so generously sent to me during this time) is more painful than I can even begin to express. He says that had I thrown him out, he, rather than lose face, would probably have taken that white charger to her house and whisked her away and then have repented at leisure once it hit him what he had thrown away for something that he now realises was nothing more than a mutual crush that got totally out of hand, and was invested with infinitely more gravity than it truly warranted. I suspect your DH has discovered that painful fact rather earlier than mine and his tantrums are symptomatic of him realising that he is and has been a total wanker and bastard, but not wanting to admit that he is a total wanker and bastard and even harder for ANY of us, having to live, daily, humiliatingly, with the fact that he is and has been a total W and B.
And I'm with you on the behaviour thing. Of course the betraying partner should behave totally perfectly when they are discovered and follow the redemption script, but as fallible human beings that is very difficult. Yes the betrayed partner should not strike the betrayer, but as devastated and similarly fallible human beings, sometimes they do - as well as rant and rave and swear. Dear god, I'm AMAZED that our poor neighbours didn't call the police on any number of occasions at the height of our battle to stay together - yes, there's an inherent contradiction in that I know - but I also suspect you know exactly what I mean.
Nearly three years down the line we have a different marriage to the one we had pre-affair, in some ways so much better, and I know that sounds a terrible cliché, but we genuinely and truly value each other and are both very alive to what we nearly lost: we still have ups and downs but they are more the normal, everyday marital ones (money, tiredness, work, DC misbehaving) and only occasionally do I lose it about 'her' and then usually because there has been trigger (she works hard to try and regain his attention through a variety of mediums). I have managed to get over the sexual jealousy but the emotional betrayal and the secrets and lies have been the hardest thing to learn to live with. Am I glad I did - yes, totally, although it has been hard-won and hugely painful. Is he glad he did? Well I don't think he could be sorrier or more ashamed. that doesn't make him any kind of paragon, because I have to live with how horrifically he behaved towards me for many months in the early days, but it does mean that someone CAN be genuinely remorseful and truly understand the pain they have caused. The secret is emotional intelligence - if your DH has it then I think there is hope for you both. If not and he is just jumping through some obligatory hoops, then I think you have to consider very carefully indeed if you want to spend the rest of your days with this man, no matter how much you love him.
Sorry, a very long post, OP, but I do really understand your confusion, pain and dilemma. The only person who can walk a mile in your shoes in this situation is you at the end of the day. We are here to hold your hand though, carry you on our shoulders when you tire, and cheer you on during this terrible journey for which you never volunteered. Our advice will differ but the outcome we want for you is the same - a resolution that suits you, your children and - yes - your DH - if he is to remain part of your life's mile. xx