Welcome to the forum brotherdan.
While I've never been to Bethel, I am a second generation JW, born in, with uber righteous JW parents (father a PO and stepmother a pioneer).
I left the JWs 4 and a half years ago, and told my husband very openly why I didn't believe it anymore. (blood transfusions, generation teaching, etc) He did not turn me in as an apostate, but he was very upset and very unhappy. We tried to make a go of it for a few years, but the situation deteriorated to the point where he asked me for a divorce (he met and had an affair with another JW woman he met at work). Apparently, committing adultery is not as bad a sin as apostasy.
They were only reproved and I'm still being unofficially avoided/shunned by all former friends because I'm inactive, but I'm not officially df'd.
After what I've been through, I have many thoughts to offer on your situation. Take it for what you think it's worth.
First of all, apostasy is not grounds for divorce in JW land. Your wife should well know this, perhaps in her emotionality, she forgot, but you might want to remind her of that. Absolute spiritual endangerment is a grounds for separation only, however, if you do not oppose her practicing her faith in anyway, and you do not talk of your religious or spiritual beliefs with her, then she will have no scriptural grounds for separation either. You could assure her that you love her and want to stay married and you will not oppose her religious practice or try to dissuade her from her faith.
I would not personally go to the elders as that is admitting they have some sort of authority over you. If she goes to them of her own accord, which she is likely to do, and they come to you, you could assure the elder's of all the same above that you assured your wife.
When my husband asked me for a divorce, he told the elders it was because I was an apostate who was opposed to him being a JW. I am apostate, but I was not opposed to him being a JW. He had asked me a couple of years previously to stop talking to him about my beliefs because it was destroying his faith. I respected that and stopped. Of course, this did not stop him from talking to me or my son, and when he did, I felt open to respond, (fair is fair) The elders came to me (the first visit in 4 years of inactivity!) and I told them honestly, that I left because I didn't believe it anymore, but I was not opposed to my husband being a JW and I was not interested in subverting the faith of any other JW's. They seemed satisfied with that and I was not df'd or even reproved. I did not get into doctrinal debates with them though, as I knew it would be pointless and would only lead to my being df'd.
Whether this works for you depends mostly on the elders in your wife's hall and how much they would look forward to an apostate witch hunt. The elders in my neck of the woods are pretty slack and like to let sleeping dog's lie. Anyway, a month later, I found out about my husband's affair, (ironically it was with the daughter of the elder who came for the shepherding visit). He went and confessed, knowing he was busted, and they were both only reproved. He had spent the previous few months telling any JW who would listen that I was apostate. His plan was to get me df'd on that and then tell everyone I had an affair so that he would have scriptural grounds to get remarried. No one would take the word of a df'd apostate over a baptized JW. It backfired on him, as I found out about his affair, but if your wife tries to pull something like that and the elder's believe her, there is not much you can do about it. It'll be out of your control, but at least you'll know you did all you could to save your marriage.
I don't know about the laws where you're from. I understand they vary from state to state. In Canada, there is no fault divorce, but there still needs to be a separation of one year, adultery, or mental cruelty. In Canada, your wife would have no legal grounds for a divorce either.
Check out the laws in your state. (And no, changing your religion is not mental cruelty in spite of what emotional JW spouses will tell you!)
From what I can see, your wife is stuck with you legally and scripturally, especially if you agree not to speak with her about your new beliefs. She could take the kids and leave but she would still have to wait a year for a divorce and it would not be scriptural unless she lied about you. If she does that, you have as much right to fight for full or joint custody as she does and as much right to teach the children your beliefs as she does. She would probably get custody though because your kids are so young and one is a baby. But there is no reason you couldn't have joint custody. Fight for your parental rights if it comes to a separation. Do not allow the JW's to dictate how your children will be taught. They will try to erase you totally from the picture but they have no legal right to do so.
In Canada, there is case law precedent of the judge issuing an injunction against JW parents teaching kids their religion because it was attempting to alienate the non-JW parent and it was so upsetting to the children. There is also case law allowing each parent the right to teach their children their differing beliefs. Much would depend on how the teaching was done. If it was done clearly to alienate one parent, there would be a better chance of getting a court order against it. Children are little sponges, and if it comes to separation and divorce, your best chance of maintaining a decent relationship with your kids over time is to fight for the right to see them as much as possible and to be able to teach them another perspective than the JW one. Otherwise, if you give up, the JW mindset would take over and your kids could one day shun you. I should point out that I spent a couple of years deprogramming my teenage son and encouraging his own doubts before I left. He is my only child and I was not going to have him be a JW and eventually shun me while I still had breath to fight it. (He is out of the org and lives with me btw)
Hopefully, it won't come to this and your wife may settle down a bit and want to try and give the marriage a chance. You could point out to her the many decent marriages of people with differing religious beliefs even pointing to example of JW's in long term marriages to unbelievers. It is possible to make it work, if both are committed. You could suggest marriage counseling. I did this but ended up going alone as any good JW is well trained to ignore any Satan influenced advice by a "worldy" counselor. The marriage counselor didn't think there was much hope. I held on a few more years, but in the end, I knew he was right. To be fair, we didn't have a great marriage as two believing JW's. We weren't very compatible in our views on most things, even before I left the org. You and your wife could fare better.
I don't agree with the posters who said let the JWs support your wife. You have a legal obligation to support those kids no matter what and probably to support your wife financially too, at least until the youngest one is weaned and in school and your wife can support herself. Your differing beliefs or other reasons for separation make no difference to that obligation. Please don't try to use that as an excuse to get out of your obligation because it will only make you look bad in court. Don't muddy the issues. It just gives justification to the JW's to say that apostates are morally corrupt.
If you fulfill your obligations as husband and father as much as is within your control, you respect your wife's right to practice her faith, you respect her right not to have to listen to your views if she doesn't want to, you support her and your children emotionally and financially, then she and the JWs will not be able to truthfully say one bad word about you other than you don't believe. That has been my experience. All the JWs I know are still waiting for my moral depravity and knashing of teeth to happen. They can wait until hell freezes over or Armageddon comes, whichever happens first. Of course, that doesn't prevent them making up gossip and stories, but in my heart, I know I did my best to save my marriage and be a good wife and mother. It takes two to want to make it work, though, and my husband didn't it want it, only on his terms.
I also don't agree with the posters who advise you to help your wife and kids get to the meetings. I wouldn't put obstacles there but I see no reason to support or help something you don't agree with that could be harmful for your kids. If she is not willing to have you teach your beliefs to the kids, I would say the same to her and let the kids decide when they are grownups. I would try to keep the kids away from the JW's as much as possible. That is not opposing her practice only opposing her foisting her religious practice upon your children. It is not fair for JW's to be able to demand one way preaching.
When my husband demanded I quit speaking to him about my beliefs, it was often after he was losing an argument that he had started! He was fine to talk about religion when he thought he would win the argument. Then when he would lose the point, he would become furious and tell me not to speak to him. This is JW one-way tolerance at its finest. if this happens to you, where your wife tries to witness to you or convince you, a good approach might be to remind her that you agreed not to discuss religious things. Ask her directly if she is changing her mind about that and will she also listen to your viewpoint? Make her analyze the process before you get into a discussion with her. Stay away from arguing rightness of beliefs with her and focus on fairness of teaching children on parent's beliefs and not another's. Or, one spouse being able to preach to the other while one has to remain silent. They will never have an honest or fair answer to this. It shows up their intolerance and hypocrisy in a way that arguing doctrine never will.
Funny story: One time my husband answered the phone at dinner time and then said, "No thank you," and hung up the phone in disgust. I asked if it was a telephone salesperson. He said "no, it was some neighbourhood church inviting him to their services." Then he said how annoying it was to interrupt people's dinner with that crap. I nodded sympathetically, and agreed, "yes, it is very annoying when people call or show up at your home uninvited to talk about their religion". My son burst out laughing, and my husband just said sarcastically, "very funny." JWs seem especially incapable of analyzing a situation outside of their own narrow frame of reference.
You definitely have your work cut out for you. Good luck and keep us updated on how it goes. This is probably the most stressful time in your life, right now, with new baby, marriage problems, and crisis of faith. It definitely gets easier eventually. I found it helps to not take beliefs so seriously, whether they are yours or your wife's. Beliefs are a bit like moods or weather. Wait long enough and they will eventually change. Another great saying I heard: "Don't believe everything you think!
Cog