BrotherDan,
I checked your other thread, and am sad to see it come to this. I hope it's not too late for you to start working together or with a counselor, but it takes two to make that happen. If separation is inevitable, try your best to have a civilized discussion first, so you both can make the necessary preparations: financial, housing, and taking care of the children.
I agree about protecting yourself financially, but you can't ignore her and your children either. Non-support doesn't work morally, nor legally. Perhaps you should have separate bank accounts, with an agreed-on support allowance you send every payday. That way both of you have a known budget to live on, and you will have a track record of supporting them should the need arise.
You also need an agreement on joint parenting. They need you as much as ever, as a regular part of their lives. Check into any classes available (or required) for separated parents where you live. I found those to be helpful; that's where I learned about the "you" vs. "us" language I brought up on the other thread.
Stay strong, you can and will see this through. You have us and our prayers behind you.