Oh OP, I am so angry on your behalf. How dare he treat you like this and then blame you too, for finding the emails. Your five year old probably has a more sophisticated logic. It's not my fault that I hurt you. You shouldn't have been in the way of me swinging a bat around my head!!!
Yy to reading "The Script" which Hellsbells linked to at the top of the page (or bottom, depending on how you read MN!)
Yy to getting a SHL and getting all that you are entitled to. Your h has been planning this for a long time, even viewing apartments. You owe it to your children and to yourself to play catch up and ensure that your needs and rights are observed. He will want what he can get but he will respect you more in the end for standing up for yourself and your family. Especially when it all falls apart with the new woman and he realises what he has thrown away.
You will feel awful for a while. At first you just fight to get through a breath, an hour, a morning. But things slowly improve. You will start to eat better. (If you haven't already, invest in milk shakes, and lots of eggs, and keep your strength up.) One day you will wake up and it just won't hurt so much. Something will catch you out and the feelings will hit you like a truck, but then you will get back on your feet again, and find yourself laughing with a friend, looking forward to something new. And in the meantime, "Fake it, until you can make it." Book a new haircut as soon as you can. Treat yourself to some new clothes. Practice looking at him with a "I don't care. You are part of our past" look on your face. Cry in private, but practice looking like someone who has got their act together. It will confuse him. It will help you.
And remember, whatever happens, you have the MN army behind you, at all times, cheering you on.