Rachel my H did the same. Its the same script, he was messing with my head for 2 months telling le they are just friends....and i read all of their ily and everything else. Yes it hurt like hell, but he does truly feel that way.
The sooner you accept the situation and take the emphasis of your M and his relationship with ow and concentrate on you and the kids the easier it will get.
Imagine a universe where there is just you and the kids, thats all you need to worry about. Nothing else is a rush at the moment. Take each task as it comes. Stop drinking, you need a clear head, exercise instead, have a bath, watch something, anything that will make you feel good. Once you have a clear head and and stop spinning, Find a lawyer to consult with, you dont tell your h anything! That you are exploring options, he doesnt need to know! This is for you and the kids so you know where you stand. Get into ic that will help build you up, i really think he did a number on you with all The cheating!

Stay strong and keep posting.