Treese, I'm sorry you are having a tough time with all of this. It's understandable. I also understand how your children feel as well. They look at their dad and see a man who lied and cheated on their mother and right now, really doesn't want to be bothered w/any of them or you. Your h will have to work it out w/them at some point. There's nothing you can do about it. They must find a way to get along, just like children who have disagreements. Your h will either figure it out or he will lose them entirely, but that's on him, not you.
I'm going to play a bit of devil's advocate w/you today.
About the mother of the child. To be quite honest w/you, I have to wonder where she's been all of this time. I'm not making excuses for her, but maybe she saw your h cheating on you once again and felt it was time to step up to the plate and make him own up to the child and his previous cheating. She may feel he needs to step up to the plate and do something for the child he's never supported and yes, he's at the age where things are getting a bit more expensive. Your h helped to create this child and he should be assisting in the support of this child as well. It is not the child's fault that he is here on this earth. He didn't ask to be born; however, he is here and his father needs to be supportive of him.
On the other hand, the ow, may have some financial difficulties now and has been in contact w/your h and is fully aware that you are in the middle of divorce proceedings. She could very well see this as an opportunity to go for the gold and get what she can from him for walking out on her and leaving her w/their child. No one really knows what is going through her head. All we can do is put the best interest of the child first.
As for the budget, thoroughly look it over and do not be afraid to speak up if it's not enough for you and your children to live on. Your h will definitely need to work several jobs to support all of his children and assist you w/the bills, etc., as well. At least he's looking at what he's going to need to do to keep things going.
Treese, I know that what I've posted isn't what you wanted to hear today, but the fact is, your h cheated a long time ago and is now having to pay for the consequences of his actions. Yes, he's even creating enough mess that you and your family are involved as well. When dealing with the financial aspects of your situation, look at them as a business deal, do not allow your emotions to rule your thinking. You are going to have to stay cool, calm and collected for what may be coming down the pike in the weeks to come in regards to child support for the ow's child.
I wish that I could wave a magic wand and make things better for you. I'm truly sorry that you are having to deal with your h's mistakes time and again. I do hope the holiday season will be much better once this hearing has taken place.
Hugs!
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.