Let me preface this by saying I don't fully understand your life or situation. I got 40 minutes in on the second link and it kind of upset me. I'm upset because obviously this a horrible situation to be in. Having small children while having some major marital bumps is like living through hell. I'm sure this is beyond hard on everyone of you guys, kids included. In no way am I trying to insult you in this.
It feels like you both are grasping at straws. When there is a big issue, smaller problems compound unless it's fixed. This will continue to get worse until you wholeheartedly try to work on it. Not to discount your feelings, but I would have trust issues too if I was surprised by a foreclosure letter and random condoms in my spouse's stuff. If I came home to people I didn't feel comfortable around in my home and around my kids I would flip my shit. Especially if I had talked about it before and was being ignored. Even if you pay the bills, she's your wife. She lives with you. Her feelings matter just as much as yours. Whatever happened before you got married should be a moot point. She still married you knowing your past.
It feels in how each of you speak and the stories you have posted, that there is little respect left in your marriage from either of you. She has severe emotional problems that are being compounded by this fucked up religion, congregation, and probably family. But you are acting like the stereotypical apostate everyone gets warned about from the podium. Dude, what about your kids in this? If she tossed your baby, threatened to down a bottle of pills, and is abusive to you, how can you keep them safe from the cult and wife if you're not around because you were hanging out with some guy instead of working on your family?
What ideally do you want to happen? Do you guys still love each other and want to work through this? Let her go to meetings but show her how much better and happy you are without them. Be a great dad. You're their shot at an actual childhood.
I'm sorry if this sounded like I was ragging on you. The baby coos and your bumblebee in the background really got to me. It hits close to home. I'm so sorry you're having to do this.