I'm not too worried about the agreement to raise the kids in the catholic faith. Everything in our history of raising them has been in the church - baptism, mass attendance, first communion, etc., so there is no ambiguity as to how they were being raised. There's no evidence for any lawyer to prove that there was any question on the matter. When I asked my lawyer about it, he told me that the courts would go by historical precedent. So even if my W were dumb enough to try to fight it, she'd lose.
Glad to hear the progress...however, you are treading on thin ice if you believe what you've written above. Your wife is nuts and you are not convinced that you deserve a faithful wife - hence, trying to negotiate her return to the marriage - so presently both of you are essentially not in your right mind.
Make sure your lawyer makes it legal about what faith they are raised in. I am telling you, if you don't, there's no way to enforce it. And if your own wife's pastor can't get through to her about her fake religion, you think that she's going to listen to you (the man she's cheating on) to be fair?
It's hardball. Get it in writing. If it's not a big deal, then having it in writing won't be a problem. If she agrees to it, the legal contract won't have to be enforced.
But if you don't have it in the contract, you have zero recourse except to appeal to your wife's Christian goodness. Which is plainly evident by her affair.
Look, I know it's hard, and it's probably something you don't want to deal with because the heart of your divorce is your wife is pretending she has faith when she doesn't. It strikes at the heart of this emotional situation.
But protect yourself and your kids.
It is worth it.
ps - When you got married, I imagine your wife told you that she's love, honor, and respect you? Forsaking all others? Maybe she'll keep the promise to raise the kids a certain way as tenderly as she did her marriage?
Sorry to be harsh, and honestly, if it wasn't about the issue of faith, I'd have no real opinion on this sitch. But it seems like you are either unwilling or reluctant to see the situation clearly.