I am generally opposed to ultimatums, but in the situation you’re describing I think a serious discussion about potential outcomes would be invaluable. Continuing to allow your spouse to be completely unaccountable is not supporting her - it’s enabling her. Thus far, you have repeatedly shown your wife that you will give in to the most unreasonable demands possible - that you will allow her to cheat on you, lie to you, break your trust, and neglect your child. You’ve told her through your actions that those things are okay. But they’re not.

If your wife is unwilling to relocate, that’s something you need to address. She shouldn’t have agreed to do so if she wasn’t actually ready to move, but that’s in the past and you have to move forward. Discuss a timeline, and agree on what steps you will both take to get into a situation you can both live with. I would suggest making marital counseling top of the list, as well as finding you and her each separate therapists (that’s expensive, but less so than a divorce). I would also suggest taking concrete steps to find a way to live together - that’s important, and you both (that includes her) have to agree that it’s vital to your marriage to cohabitate. There will be other issues - she has to agree to no more extramarital affairs. If she can’t get on board with this, and can’t show you real work to make it happen in a reasonable amount of time, you have to make it clear what the result will be. Tell her clearly that if she can’t bring herself to work on your marriage, you will file for divorce and custody of your son. Mean it. It’s not an ultimatum, it’s a true statement of what you will need to do to protect your own mental and emotional well-being.

Tell her you love her. Tell her you want to be with her. But know you can’t force her, and no amount of “support” will ever make her do anything she doesn’t want to do. She needs to know that her actions are unacceptable and you won’t continue to live like this, so that she can finally make a real choice about her life. Up to now it hasn’t been a choice for her, because she knew that you wouldn’t require a choice. Require one. You’re valuable, you’re important, and you deserve a partner who cares as much about you and your relationship as you care about her. You’re a person in your own right, not just a support system. Your son deserves at least one happy parent - right now he has none. Try for two, but if you can’t make that happen, at least make it one.