Hello dreaming. I have read all of this thread and my heart breaks for you because I have been in this position however, my now-husband's affair resulted in a baby. That was 7 years ago (we have been together 9 years) and we got married 5 years ago and are very happy. You will be happy again, perhaps with your husband or on your own - but you WILL be ok, promise.
Firstly, I would say go easy on yourself - you will look back and realise that this was the car crash period. In the immediate aftermath of my husband's affair, I could barely function and would agree/persuade myself of anything because the thought of life without him was terrifying. Only when the dust has settled and you have got some breathing space, will you be able to think clearly. If you don't want to do something (like the DCs going away overnight), don't do it. I would strongly consider physical distance from him though (moves out for a time, contact on YOUR terms. if he goes to stay with her, then he's a played his joker, frankly). This is a crisis in your life and you are allowed to call the shots. Rest when you can, eat and vegetate, take it one step at a time. All the Beyonce shit can come later.
Secondly, I would really consider telling a friend. Whether you stay in the marriage or separate, this is a long haul situation, I'm afraid, and you will need support to have anything like a good shot at it. I was surprised by how accepting people could be - there aren't many people who haven't experienced something horrific in their lives and you will also be surprised by how many people have been through this scenario themselves.
Thirdly, I think you must work on accepting that they will have had a full sexual relationship; people don't have affairs because the chemistry isn't amazing and their groins aren't on fire. Your husband will deny this (the pattern of only admitting to what he knows you can prove is spot on) but unfortunately until he is full and frank about this, it will be very difficult for you to accept apologies and forgive him - or at the very least accept that he has finished the affair and wants to move on with you. I don't personally think you need to see the agonising texts, emails etc - I can promise you that they will contain all the usual smutty, gooey shit that you would have sent your husband when you first met and will only turn your stomach and serve to torture you needlessly. But I must say that unless your husband comes completely clean, I don't think things can truly move forward.
Which leads me to:
Fourthly, your husband must quite simply agree to all your demands and nothing less. For me I demanded that my husband would be in contact 24 hrs a day for the rest of his life (he is, but it is not an issue now - more anon), go to Relate with me, go to counselling on his own (family issues/stress/anger) and no more lies. Ever. This was even more complicated as he wanted to support her in her pregnancy (as much as you can support someone you don't really know, only see late at night, don't actually want a long term relationship with let alone a family). Like I said, car crash. Looking back, those first 3 months were horrendous made worse by the fact that we were living abroad at the time and I felt very excluded by my social group who seemed disgusted by me because I wanted to stay with him (understandable yes but didn't really help me when I felt I was breaking down). If he works with her, he must change jobs, his phone must be freely available, (I demanded that my husband call her on speaker phone - I still wince at the hurt and betrayal in her voice when he told her exactly whose side his bread was buttered on) there must be no squirming and he must agree to answer all your questions truthfully (he will try to 'protect' you from the gory details ((unless he's an utter sadist - unlikely)) but examining some of the gruesome detail is a way of processing the experience so that you can then move on. This however may take a few weeks to hammer home but he is probably trying to extricate himself from her and is not thinking straight - in short he is utterly fucked up right now, I'd say. But ultimately, when the dust settles he must willingly do all he can to make you happy and regain trust - no compromises.
Fifthly, forget about her. She is not a monster. Unless your husband chooses to be with her, which let's be candid, does happen but not that much given that it's not actually that sexy shacking up together with less money, someone else's kids to deal with on your lovely weekends, a man who's lost his children and the excitement of illicit sex long gone, oh and the mundane domesticity (towels on floor, spending hours on the loo - men are so sexy) which is a serious relationship, she does not need to concern you. It is hard not to have a film reel in your head of all those moments that are torturing you, like some sexy French black and white film; the reality is not half so smouldering and sexy so de-heat those thoughts. But disengage from her - as they say, resentment is like drinking poison and expecting the other person to die. Whether you stay in your marriage or not ( and your husband sounds like he's shitting himself that you won't), you do not need that woman using up your energy; he betrayed you, not her.
Sixthly (!), in terms of harbouring resentment and grudges, I don't. Believe me, I am amazed by this as I was always very jealous and no second chances. But what happened to us was so huge that it went beyond platitudes. I very soon realised that this woman and the baby would be in our lives forever and, if I wanted to stay with my husband, I would have to truly accept and forgive. This would not have been possible if he hadn't enthusiastically agreed to every demand I made. It took a whole year before I felt normal again and the first few months were hellish. A male friend whose wife had cheated on him (although he then ended the marriage) said that he could only move on by mentally closing the door on the horrid images and thoughts - they only hurt YOU in the end - the other two aren't agonising over who made the first move and what sexual positions they did. It takes discipline but if you want to feel clean in your mind and not have his betrayal keep pushing its ugly way in, it can be done - whether you stay with him or not. I now feel strong as a woman - I've looked the abyss in the face - and I didn't compromise my morals either (I forced my husband to go to a solicitor about access and maintenance as I knew we needed legal provision for the baby in the midst of the emotional ten-car pile up and my husband, and her if I'm honest, just wanted to stick their heads in the sand. You need to be equally pragmatic about protecting yourself financially and seeing a solicitor). I trust my husband as much as any one can trust another human being, which is to say that human beings make mistakes - sometimes huge ones. I have not felt the need to look at my husband's phone etc for many years now and he is in a job where he commutes at the weekend ( we both travel a lot for our jobs). I have no issue with this but only because he has bent over backwards since the affair to make things right with me and I trust and love him.
I sincerely hope you aren't awake reading this but if you do get to read it I am sending you a lot of love. X