I’m so sorry to hear about this. Some of the comments made were not that nice (it takes two to tango), and there were many that were good. I think you are doing the right thing supporting your children and not painting Daddy as the nasty bastard he is. Even if this doesn’t work out, he is still their father, and as they get old enough, they will learn the real story and form their own opinions. For now, they need both of you.
Mosca mentioned paying the bills. Thats a good idea, but you should see a lawyer immediately. He left you for another woman. Even if this new relationship doesn’t work out for him, he has shown himself to be a cheater. If the two of you do not get back together, you need to freeze his assets NOW to protect yourself and the children, and I say this not knowing if you are employed, have a high or low paying job, or are a stay at home Mother.
See a lawyer and let that wandering philandering husband of yours know that his affair is going to cost him dearly, and he is not going to leave you and the kids on the short end of the financial stick.
Also, if he comes back and tries to make up, please practice safe sex with him if you even consider doing it. Who knows where he has been fooling around and what he has picked up. You don’t need to have him hurt you by passing on something else besides the loads of hurt he has already dumped on you.
Good luck, and I hope you have friends and famaily nearby to give you the support you need and deserve at this time.