How do you give advice for THIS nonsense?
You already know that you need to find a place to live that you can afford, that allows you to meet your financial responsibilities for your children. Being homeless, and claiming that you cannot afford to support your kids, is going to confirm your wife's existing belief that you are not a solid, reliable, financially supportive husband and father.
On 4th March 2013 you wrote, "I have been unemployed/underemployed for over 3 years. I've been separated for almost a year in the hopes that I get back into a good-paying job that will support my family. Hasn't happened."
You were unemployed for three years while your wife was working through her last pregnancy, and you moved out never having shown her that you were back in a job and able to support the family. Now she's had to take you to court for the child support that she was clearly due, and the effect of your being made to pay this has been for you to become homeless and unable to see your kids.
This is a disastrous image for you to be projecting to the woman that you hope will go back to you, should her current relationship end. From her position, you are no more attractive than you were when you were unemployed and living with her. It's no good (silently) blaming your financial plight on the fact that you do not live with her in the marital home. If you want to be seen as an appealing prospect, you need to resolve your financial problems and show that you can support a family.
Your wife is a lot younger than you, and as such, she expects you to be able to support her and look after her. Indeed, financial support is a key emotional need for many women, but Dr Harley has observed that for women with a much older husband, her husband's reliability and being generally supportive is a key need that she has in her marriage to him. You let your wife down on those aspects when you were married, and you are still doing so.
10th April 2013: "I spoke with a lawyer at Legal Aid this week and he said that she will probably get the house. We have a business as well that we each own 50% of, and that will probably be sold and split. She works at this business so she'll probably be out of a job. She is a hairstylist, so she'll just rent a booth somewhere else and her clientele will stay with her. However, I am quite confident that she will not be able to pay the mortgage on the house by herself without having to work a LOT. She will end up losing the house and renting a crappy apartment somewhere."
You thought that she would not be able to to afford to stay in the house and would be forced into a shabby apartment after you left, but she has managed to keep her home together, despite having a baby under a year when you left, and having to pay for childcare once you found work.
She is managing on her own quite well (with the financial support that you quite rightly must pay for your kids), so why does she need you back? Can you see how becoming homeless because of child support makes you very unappealing?
And as for this "affair":
You left your wife when she had not long had a baby: "When I packed a bag and left for a couple days to get away from the pressure, I did so with the intention of coming back after she cooled off, which I did, but she changed the locks on me." Nearly a year later she filed for divorce, and about 2 months after she filed, and about a month before the divorce was final, you saw a man who was clearly intending to spend the night at your house.
Clearly, since she was still married when she began seeing this man, this is technically an affair. However, you have spent your whole time here focusing on this "dirtbag" OM, when he was NOT the reason your marriage broke down - the reason was your own unemployment, anger, excuses and finally moving out. He did not come into the picture until after you had moved out, and after your wife filed for divorce.
He is NOT the reason you are not with your wife. The reasons for that are the original reasons the marriage broke down, and the fact that after you left, you went through not paying financial support for your kids (you called this Plan B, when you had not done anything like a Plan A), you had anger problems about the fact that she would not have you back, and all the other issues we raised with you on your last thread.
If you continue to focus on this "OM" and his faults, I guarantee that you will miss the bigger picture, which is YOU, and the ways you did not, and still do not, meet your wife's needs.
Your wife finds this man, with his "four arrests" (which are not the same as convictions) more appealing than you. If you want her to consider going back to you IF her current relationship breaks down, you will need to think about why you are not easily displacing him in her life.
Since you came here, you have been waiting for that affair to break down, as if it inevitably will. The problem is that it might not, and even if it does, there is no obvious reason why would your ex would go back to you. You let her down and abandoned her with two young kids, and she survived that. Why, from her point of view, does she need you back? Have you given her a reason to need her?