Here's going slightly against the grain here, though not entirely. I mean, if you want to try to work things out, that's not up to you at all anymore. You just get to let her know, then leave her alone until she speaks to you.

That being said... yeah, you emotionally fucked her up, but you gave her a disease dude. What insane state of being put you in a place where you could sleep with a person who had an STI, then throw that back at your wife? You absolutely NEED to seek therapy no matter what the outcome. Was it a prostitute? "Massage" parlor? Drug/addiction related? Or was it an actual random one off that just coincidentally had something? No matter the answer, you need to address the root of the problem.

Here's the other thing... many of the people telling you how horrible of a person you are for this have been hurt by something similar being done to them. Consider their words to you as a mirror of how you made your wife feel, just to get an idea of where she's at.

The custody thing no one has a right to judge on without knowing details. Arguments can be made, but this isn't about your child... I truly hope you can maintain a relationship with them, though.

Now... here's the part I might get some heat for. You're not a monster. You're not a piece of trash. You're a guy who made a mistake with some pretty grave consequences, and yeah, you get to bear most of these feelings on your soul because an apology won't fix this, no matter how sorry you are. That being said, you need to change yourself before trying to be in a committed relationship because it's not fair to anyone else if you promise to commit without being able to see it through.

Good luck, man. Sincerely.