Before I get into the update, I need to clarify something that many commenters were asking about on the initial post. I edited that post as well, but decided I should put the explanation here as well. Many people have been asking how my wife getting a job was able to pay for a nanny and me reducing my work hours slightly. The answer is that we live in the northeastern USA, where minimum wages are good (relatively speaking), and that "nanny" was a poor choice of words on my part. She's more of an informal babysitter, not an official job. She's a college student who wanted to make some money while taking online classes, without dealing with the hassle of getting a real job. My wife makes around $16 per hour with a standard 40 hour work week, while we pay the babysitter $10 per hour for five hours per day, five days a week. After taxes on my wife's income and paying for the babysitter, we have around $900 a month left over that has allowed me to reduce my hours slightly.
Now, for the update. I called in sick to work today, which is something I rarely ever do, and asked my wife to do the same so we could sit down and talk about everything. She agreed, and this morning we had a long, heartfelt discussion. I told her that I was sorry for what I said in the heat of the moment. I don't want to divorce her, I was angry and hurt and wasn't thinking about the damage threatening divorce would do. I told her that I understand things have been difficult for us the last three years, but I was shocked that she would be "sorely tempted" to cheat on me after just six weeks with some random guy at her job. I told her that having been the sole, or at least the main provider for our family pretty much the entire time we've known each other, I felt like I wasn't being appreciated enough for the work and effort I've been putting in.
She said she felt the same way, that she felt like she was struggling thanklessly since I was never around to be with her. I told her that that was only the case because I had to make enough money to pay for the kid and the house she wanted. (And before anyone tries to twist my words, I love my son dearly. I am not simply "putting up" with him because she wanted to keep him.) If I took less overtime to see her and help with the kid more often, we'd have trouble keeping the lights on. We both agreed that we needed more time with each other at home, but talking out how to make that happen took awhile.
Eventually, I told her that I stand by what I said to her when we first bought the house we are currently in: it is too much house for us. It's a two-bedroom, two-bath house with more area than we need, and the mortage and property taxes are too high. I brought this up when we first looked at the house, but my wife insisted that this would be the perfect house for our family to grow up in, and that once it was paid off, we would be set. But seeing how much we've struggled to afford this house while slowly falling apart physically and mentally, I think she understands now that it's too much.
After some prodding, I convinced her that we need to start looking for a house to downsize into. Selling our current house will give us enough cash to pay off the mortgage, though not by much. Once we're in a smaller home with smaller expenses, I won't have to work as much, meaning we can spend more time together as a couple and a family. She told me that she "just wanted [my name] back," and I honestly almost cried hearing how much she meant it. I was so focused on work and paying the bills that I lost sight of what we needed as a couple, and our marriage very nearly imploded because of it.
The final issue to address was her job, and more specifically the scumbag who was hitting on her while knowing she was married. Given our current financial situation, it would be stupid to make her quit her job and go back to staying at home, plus it would probably only make her feel trapped again since she only recently got back out into the world after bring a SAHM. However, I can't stand the thought of that guy even looking at my wife, especially since I know she harbored some sort of interest at some point, even if it came from loneliness and desperation.
I told her that at the very least, she needs to report the guy to management/HR and ask for different hours so that they are never in the building at the same time. If that happens, then there's no reason for her to just quit, but if that doesn't happen, then I'll be helping her look for a new job immediately.
Things are still difficult right now, but as I type this a couple hours after the conversation, I think we've pulled back from the point of no return. We're both just taking the day to calm down and think rationally about what needs to happen to get our financial and personal relationship back on track, but I'm hopeful. Thank you so much to all the people who gave advice and constructive criticism. I know lots of you suggested couples' therapy, and while I'm considering it, that's another big expense I don't want to take on right now unless it's absolutely necessary. If things continue to improve between my wife and me, then I won't waste the money, but if things start to stagnate or get worse again, then I'll bite the bullet and suggest getting professional help to her.