So sorry you are going through this. I agree with some of the above posters, it all seems a little odd, but the truth will out, it always does. LouP is going through a similar thing, H has left, she is pregnant, OW is pregnant..... there are some awful men out there it seems.
He needs to go, you need to arrange simple basic contact for your children, you need as little contact with him as possible, dont let him see the kids in the house etc for your own sanity.
You also need legal advice asap, contact Working Tax Credits and tell them that he has left, contact Council Tax to get your single person discount. It all sounds a bit clinical, but it will help you to do positive things. If you rent then find out about housing benefit etc.
You will get through this. Im now six months on from STBXH walking out after an emotional affair with OW. My divorce is due any day now and I am in a much stronger place than I was 6 months ago.
You will get plenty of support on here, but please do contact your best friend, closest family member etc. Go to your doctor if you need to, just make sure that you get plenty of support. If you have a Sure Start Childrens Centre near you, then go to them. They can offer fantastic practical advice and support.