If I don't file, yes I have access to all the money and things are stable, but knowing he essentially has a girlfriend while I sit home and keep our family running is killing me. I guess I'm just looking for concrete advice.
You have one of the better people who've ever posted here as far as understanding your situation. I agree your assessment 100%. And above is the crux of it.
I think most advice given, even my own, is based on the predictability of cheating. It seems you've read quite a bit, and I know how difficult it must have been as a single mother, educating your children, with essentially no support from your husband except the finances. Even having to comfort him for most of the past year.
I think first of all you should try to stop feeling pressure to do anything right now. You can keep going the way you are for the moment.
I think you should hope for the best and plan for the worst. I think you have some time to prepare yourself for the future.
You mention a lose-lose situation. Unfortunately, sometimes events occur that are lose-lose. Things happen to us, accidents, health issues, that we have little control over. Your situation with your husband has been a lose-lose. Maybe in the distant future it will all be for the best. Time will tell.
So I think you should stay put for the moment, and make a plan. Prepare for your future and your children. You had a plan before this, your husband would work, you would stay home and educate the kids. Due to any number of unfortunate events, that plan may have been damaged. It turns out infidelity has happened, and your previous plan for the future is not going to work. So you need another plan.
I think the first thing you need to do is to get a consultation with an attorney. To see what are the rights and obligations of you and your husband regarding the other woman and your husband's other child. Find out what you should do now to maximize your future. Consider if you have to keep track of your husband's expenditures related to the other woman? If you should be tracking his time vs. your time in the house and with the kids? Should you start doing something for preparing for the workforce? What will your husband's rights with your kids be regarding the other woman and the other woman's kid(s)? Prepare that your husband can't walk away, so is committed to that child forever. Your children are going to know at some point that they have a sibling with another mother. This isn't going to ever go away, let that sink in, go through your stages of grief and get to acceptance. Maybe you need help with a counselor. Maybe you have someone who can support you emotionally and yet help you remove emotion to get the best outcome for you and your children.
I think the affair will end. Maybe in two years or less. I think the other woman will meet another guy in a gas station or a convenience store or wherever sooner or later. But your husband still will be connected to the other woman forever through their child.
What I am thinking is to register the kids in school next year. I think this time of year is to register. You can check what is required and when and prepare. In the meantime, prepare for the workforce now while you don't have to do anything yet but prepare. Then step-by-step put together a plan that will work, the best plan that you can. Keep in mind that many times I've seen, you can get a better divorce settlement while the cheater is still all deep into the affair.
I think everything will stay the same for awhile, so why make your life harder than it has to be. The problem is as you've said it is killing you. That is partly an outlook, an expectation, a hope or wish, that I think you should try to accept very well might not happen. You can be separated in your mind. You don't see him that much now.
I think it's find to tell other woman's mother. I think it's good that all parties know the truth. I think you have to be realistic, the other woman wants the future that you wanted, a happy family happily ever after, and the other woman's wife probably is going to want that for her daughter, and your husband's mother is going to want that for her son. I think if they are smart they are going to want you to be happy, too, and your children. Just one big happy combined family, that's what everyone else might want.
In the I Can Relate section there is a thread on infidelity with other children (OC). It says, "This ICR thread is only for BS's or madhatters whose partner's infidelity has resulted in a pregnancy or potential pregnancy and/or an OC situation." So maybe you can take a look in there.