Hello, I've found you.
It really is awful - and everything you learn now is going to hurt you even more. I promise you this most awful of stages is just that: a period of time, but eventually you exhaust yourself and you move on.
It's bad enough they lie, but then when you find out not only have they left, but they continue to lie, they insult your intelligence and your gut instinct.
And of course, there's going to be consequences. What I've realised is that when cheaters think with their sexual anatomy, they don't realise that there's the "fees" to pay after. Court fees, alimony fees, kids fees, plus more bills, plus the cost of wooing another. At least prostitutes are upfront about this. I'll leave you to infer of that what you will with regards to integrity and decency.
He's got to still pay the bills, and feed the kids. So you need to get yourself down to a solicitor if you can afford one, or the CAB if you can't. Talking to people about divorce does not commit you to getting one right now, but the sooner done, the sooner mended.
And don't worry about crying your heart out to a solicitor or a CAB worker - they are more than used to it! They are they to help YOU and your children, now that the person who you were depending on has abdicated.
He has made his final decision over your marriage. From now on, you're in control - you get to decide. Of course, he needs access to the kids - but there's plenty of family around to make sure he doesn't get to see you.
You are not visible to him for now. Lick your wounds, feel sorry for yourself, hate him and do not beat yourself up for him going elsewhere. His choice + His actions = Your hurt.
Aside from that it's No Contact (NC) for you, I'd suggest. At first, you'll really want to just hear anything, but it's self-discipline from now on. You've got that in spades anyway: since you've managed not to shag anyone else just because your husband's been horrible for weeks (!). You're amazing, really.
After a while, they realise that they can't control you, and they miss some things, and the biggest hurt:
They realise you don't want them back.
From now on, cry if you need to. Go out with friends, get a haircut, do fun stuff with the kids. Watch any TV you want. Get rid of any bits and bobs around the place into a safe place.
Whatever you do, do not do anything that'll bite you on the arse later. So no criminal damage, no peeing on his shirts, no nasty emails or facebook messages. No badmouthing.
You prove you are the paragon of virtue by your actions. He's proved he's not with his. Don't upset that balance.
I know your pain first hand. I don't know you, but I know I wouldn't wish it on anyone. You're not alone. We're hear to support where we can.
Take care and be nice to yourself.