My son is driving me nuts

Alas, this seems like you need skilled legal argument more than psychiatry.

Perhaps this can be pasted to a new thread at "off-topic", but I'll have some questions right away:
- Are the kids cooperative in the secrecy? Do they avoid you? 
- HIPAA denies access to adult health records if they're over 18.
- Has a court specified who makes medical decisions for the kids? 
- Can you go directly to the kids' doctor for this information?
- How have you obtained the minor reconnaissance you have? For both the gender dysphoria and Munchausen.
- Of all your kids, are any of them a weak link? I think I'd try "divide and conquer". One kid has a pleasant functional relationship with the father, it gets hard to keep the fable that you're a monster intact. That kid may have info even the mom doesn't. Probing early on will get detected and potentially labeled as ulterior motive, sneaky, underhanded and evil, though. So it'll need to be an organic conversation. This won't be quick.

Active in the LGBT community, my daughter befriended at least three transsexuals, so I may have a smidgen of second hand insight. The absurd North Carolina bathroom idiocy had me do some extra research as well.

The process is long and drawn out. Unless you've been in the dark a long time, there's lots of time to look for details. Responsible medical/psychiatric personnel look carefully for any other rationale / course of action because the science of sex reassignment is woefully primitive in the 21st century. You better darn well be absolutely sure you want to do this thing.

You speak of "extended" child support. This suggests beyond age of 18. Is that your youngest about to age out?
Can you plead Christian and invoke 1st amendment rights not to change the body God gave your kid? (Then voluntarily help in a capacity YOU choose to.)
At that point, the ex doesn't make medical decisions any more. Nor is she responsible for medical expenses. It strikes me as odd that her decision to help beyond legal requirements should extend to you. Her morals and emotional prerogatives should not carry the force of law, I wouldn't think.

The Munchausen thing. If they reach age of majority, I would think offering a place to stay should allow escape from medical harm inflicted by the mother. If the child sees the mistreatment as beneficial, probing questions to sow seeds of doubt allow the victim the material with which to have an epiphany later to get out from under a controlling abuser. (assuming that is indeed the case.)

Like your own services, these have been free, and you get what you pay for, so...caveat emptor.

Try the term ‘Munchausen by proxy’ which refers to the fabrication of ill health by a third party. This is a much more common phenomena in the field of child health than has recently been reported but is becoming increasingly recognised or at least considered. I hope this emerging recognition (here anyway-I imagine it is global as everywhere pulls on the same evidence base) advantages you in your court proceedings. 

Updates. He is still in his lousy job and another round of redundancies beckons. He talks of fetting a sweet payoff and then taking time to find a job. Again.
He has a girlfriend!!!!!!!! I hoped such responsibility might make him grow up but no sign yet.
It is a bit like a sexless marriage I suppose. He clings on against all hope and experience in fear of finding something worse.

Interestingly we are having a family pow wow tonight. He says I am full of anger and rage. We need to sort things out. Perhaps he is sensing my change of attitude and trying to put that genii back in the bottle.

Getting crap from his kid was new. Granted it may have happened before or all along, but you're on point with this whole boundaries thing being critical.
Self-respect and valuing what you want has been a recent trend we're seeing and it isn't just teh wife who's dismayed by his investing less in others.

Perhaps, his son is copying his mother's verbal strong-arm tactics out of the horrific realization his dad has turned a corner and has limits now.
Mind you, service to others is vital to life's purpose. Hedonism is a road to depression, but when that service to other crowds out one's own desires entirely, you can also get long term blues. It becomes a same old-same old tedium uninterrupted with moments of novelty and amusement. Burnout. If you burned out long ago and didn't notice, I think you get Lessingham. A person feeling unworthy of "me time".

Or, I'm assuming too much.

As for wanting a refuser? When the vows say that's all you can have, and sex is a biological drive, you're going to want even someone that lacks appeal.

If you're hungry and the only thing in the  cupboard is canned okra and unsalted rice cakes, you'll still want to eat, even though you'll lament that what's available won't be that great and may remind you of much better meals of your past. Conventional wisdom is that men get "hungrier" than the ladies. It's possible you've never felt the same intensity of "hunger". Maybe can't? 

I agree about anger. As a English man I have great difficulty dealing with my anger, seeing it as a negative and destructive thing. But it can be positive. It is a gauge of feelings. Oh dear, you refused sex, that makes me very peeved verses I am really sngry about your inability to comit to a sexy marriage!
I have to accept my right to be angry and express it in a non destructive or violent way.

Agreed, anger should not last. I sort of envy people who can get angry easily and end it easily. For me, since I do not allow my anger to vent I fear it and fear not being able to end it