Sara, I am so sad for you. I am truly amazed how you reacted to that news. I would like to give you a big hug, it's ok to cry... it's ok to feel down...it hurts so much.
Contact yourself a lawyer but don't tell him anything, starting now keep your cards for yourself, advice given to me by a very dear friend (Insha Allah to her), don't believe any of his promises unless they are on papers and signed in front of a judge (her husband cut his kids' phones, credit cards and stop paying for their medical schools the day after his got his divorce, he "loved his kids"). Keep all the messages and keep a journal about his interactions with the kids, you need to protect yourself.
Don't file yourself or assist him if you don't want one, let him do the work! There is no magic potion. It will get worst before it will get better for a few months. He had already that idea of divorcing. Stop blaming yourself, mine started to say very mean things to me "it will never work out between us, I will move out soon" every time we had what he called an "argument", which was more "sorry I disagree, please don't talk that way to me", after he realized I was not going to be a mat anymore, I was not going to let him control me and the kids the way he wanted. I stood (while crying in the shower), but I didn't back up, he is still at home. That's just a game they are playing with us. Remember they are lost and they need to find a way to blame us, if he really cared for you at that very moment he will try to communicate more not to mumble while being adressed... Remember he is the one who cheated. He is the one who decided to hurt his family. Stop blaming yourself..
Don't expect him to be nice with you, that's where the boundaries are for, specially if he wants to keep living with you until the divorce. He might get nice sometimes but then be very careful, usually that's when they are looking for something or just doing a touch and go, to evaluate where we stand. Testing also their power. Let him have the space he needs but don't accommodate him, he needs to figure out how to live by himself (laundry, cooking, cleaning, groceries... he wants a single life, ok, ) and let him have the 3 kids a full day without you (reality check), establish a schedule (inform him by email/messages so it is traceable.)
Good night dear Sara,
Me 52+ WH 57+ Married 20 + Piecing since 2016 (ready to give up...)