You feel powerless over your situation because you refuse to exercise any power over your situation. In reality, you have the upper hand and could have chosen to move your son home at any time. But the longer you stay, the harder it will be to move your son back to your home state. Sometimes 6months or 1 year are milestones for establishing residency, either officially or unofficially.
You previously said:
you made more money and had better career prospects "back home",
your and your wife’s family live back home – you have no family support in the new city,
your wife travels a significant portion of the time so you are by default the primary parent,
she has detached emotionally from you and to some extent your son,
she immediately started having an affair with an older, married coworker,
no one knows about her affair but you,
she moved out from your established home,
she started drinking and her new place is a mess,
she is lying/avoiding telling her family about the separation,
she has talked about moving back home but not made much effort to do so,

I look at these things and I think you have all of the power. If you wanted to, you could get primary custody, you could destroy her affair, you could ruin her job, you could move your son back home. You have the power to do any of these. You should definitely not feel “weak and powerless”. You have all the strength and power because she made a ton of bad decisions while you were just being a good dad. The choice really is up to you. You will decide which decision to make, and that is not being powerless.
So, if you do decide to move back home, then here is how you can do it:
1. Document how much time you have your son versus your wife, document things that you do that make you seem like the primary parent (overnights, contact with school, doctors appts, etc). Prove that you are the better parent, the primary parent by default. Show that due to her schedule, she cant be a sole parent – she needs you but you don’t need her.
2. Consult attorneys in your new and home locations and plan your course of action. Try to get any legal basis as a primary parent. If you get primary legal custody then, hurray, you’ve won. But this is a long shot. What you will probably have to do is just up and move home on your own volition. She then has three choices, a. Do nothing but hiss, yell and threaten, but she keeps her new single life and settles for occasional visitations back home, b. quit her job or get a transfer to follow you home, or c. file emergency custody orders to try to force you to return your son.

Which do you think she would do? I would put money on a, and once the shine of single life wears off, then b. Especially if she sees that choosing c is an uphill battle:
3. So, step 3 is make her potential fight an uphill battle. Create a position of strength to keep you son in your home city. Courts will side with preserving the status quo 10 to 1. Make the status quo be your son living in your home city. Slow play and delay legal proceedings. Make things expensive and difficult for your wife. Document why your son is better in your home location. Document your history there. Get a job or show your better career prospects. Get you and your son involved in school, community events, church etc. Reunite with his friends. Show how much family support there is. Get letters of support from your family, friends, schools, doctors, ministers etc.

Finally, go for the slam dunk: get her family on your side. You mentioned you have a very good relationship with your FIL and that your wife has either not mentioned or lied about the situation to them. Well, you talk to him man to man and set the record straight. Tell them the truth and show them evidence. She is not acting like herself. She all but abandoned you and your son after the move, she was going on trips with another man while you were unemployed and watching your son, she started drinking, her apartment is a mess, she detached not just from not just you but your son, you don’t know what is going on at her place but you are worried about him when he’s over there. Almost all grandparents will want what is best for their grandson when its clear their child is not behaving as a good parent, and what is best is that the grandson moves home near them. You can even make the case that moving home is what’s best for their daughter, too.

So, she can try to get a court to award her primary custody. But that would mean: moving the child, finding multi-day child care for when she is traveling (fat chance) or forcing her to find another job with flexibility and no travel, taking him away from all family support, going against the recommendations of important people in your son’s life, possibly your wife’s own family, ruining your career prospects.

All this so that your wife doesn’t have to move home. How do you think a judge would decide on this?