After reading the old thread and this one I would be asking myself a few questions if I were in your shoes.
1. Are the children mine? As painful as this question is your old thread talked of some infidelity on her part.
2. What is my moral obligation to the children? What part do I want in their lives? How do I want them to view me? What part of my childhood that was not good do I want to try to protect them from? What good things do I want to teach and show them?
obviously the legal aspect of your financial obligation will be decided by the courts- unless things have changed your ex did not work and has been home raising children and will be for many years, so your financial obligation will probably include supporting her as well.
3. since this is an early retirement forum and I assume that is why we post here, what can I do to move forward in my own financial security?
4. Where do I see myself in five years, ten years, fifteen years? At this time you must be about 28 so you have a lot of years ahead of you.
just because you made mistakes in the past (like most of us) doesn't mean you have to keep making mistakes in the future.