Breaking up a family isn't always a bad thing and more often than not it's how the break up is managed that affects the kids in a bad way.
My mum and dad split when I was 5 (I was the middle child of 5), it was the best thing that my mum could have done for us and I still believe to this day that she was stupid for staying with him for 14 years 'to not break the family up'.
Your kids won't be happy anyway with a depressed mum who is walked all over by thier father. He will cheat again and all that heartache you went through will happen again, and again your kids will be affected by the atmosphere in the house, you being broken hearted etc.
He doesn't regret his actions at all, if he did he wouldn't try to twist it round and lie, making you doubt yourself and feel crazy. He's a cruel, manipulative liar and he's done it again because he wasn't sorry about last time. How can you contemplate staying with a man who has put his ego/sexual needs above you and your children? Because that's what he has done and don't think for a second that you and the kids mean the same to him as he means to you, actions speak louder than words.
If you want what is best for your kids, leave now and start to rebuild them a stable life while they are young. Honestly, mum and dad splitting up is not the end of thier world. Please choose to give yourself and your children more than what you have now. When someone loves and respects you they don't treat you like this and if you stick around for more that is what you will get, more lies, more deceit, more heartache and pain.