Nothing like a know-it-all teen telling you, the parent, how you're screwing up their lives. Fuck that. Mine tried that shit and got a very long earful about gratitude and bratitude. You are the parent, no matter how much the opposition is demonizing you to your kids, and you have to stand your ground and not let them disrespect you. You can still be "mild tempered" but let them know dissing you is not allowed. You are still the parent regardless of your religious affiliations, or lack thereof. This is a terrible combination: the terrible teens and the arrogant org. I found that just continuing to be there, to listen, not to go all judgey or ballistic had a good long term affect. You have to be the rational one so if/when the time comes they see behind the curtain, they'll know where to turn for help. You have to play the long game. Even if they get dunked, you know it's not the end of the world.

Do you have shared legal custody? If so, you might be able veto the homeschooling. What does your custody document say about who makes which decisions? Sounds like you ex has primary physical, but you should also have some rights, and if so, exercise them for the good of your children's future. Their frontal lobes aren't fully developed yet and still need the guidance of a rational adult. I said rational. Doesn't sound like there's a lot of that where they're being influenced most. From my own experience, even if they're still stomping around and sulking, they can respect a parent who watches out for their best interests and doesn't cave in the face of a tantrum. (Theirs or the other parent's.)

As far as devaluing yourself: fuck that, too. It's not easy being the heavy, but it's all part of the parental landscape. The first time I heard, "I hate you!" I said, "Great, then I'm doing my job."

I hate it too. I tried for years to allow them to make relationships at school allowing them to have them to the house etc. They didn't bite and now I have no plan.

Maybe it's time to take a break and go without a plan for a little while. Just back off and hang out with them and not talk about anything. If they bring it up or try to get into it with you, you could just say that you've already given your opinion and how about those Diamond Backs? Think they might win the pennant this year? I've also found that being a little standoffish changes the dynamic just a bit. Makes them realize you don't exist just to serve them.

My fear is them learning the hard way

Yeah, that's a hard one for a parent, but it's part of life and you can't protect them from everything. Chances are on your side that they're more likely to leave than stay. You just have to focus on your own life and set a good example for how getting out of the org is beneficial in so many ways. Go do some fun and productive things. Don't let them see you sitting around brooding. They will take notice.

Anyway, those are my thoughts based on my own experience.