I’m sorry you are going through this.
As others have said, vasectomies are not 100% “fool-proof” either. I had a friend in high school who was the happy “surprise” that followed his own father’s vasectomy. It happens.
Personally, if things were that dire for the prospects of my wife’s health, I could not in good conscience do anything that would jeopardize it. I would need to be 100% sure. And the only 100% certainty is abstinence (as much as that stinks).
I’d also be extremely hurt if my wife gave me an ultimatum and threatened divorce. That is not the action of a loving spouse. Do you truly think she would follow through with that threat or is it just the emotion/aggravation talking? It is very disrespectful for her to put you in such a situation. Love is unconditional. It’s not, “I’ll love you if you do what I want you to do and only if you do what I want you to do.”
This is something that jumps out to me, along with something you said earlier, OP.
You said that she had brought this up after kid #3, but then it was discarded/set aside until kid #4 came along. You needn’t answer this, but what happened between #3 and #4? Is it possible that she feels as though you ignored her fears and worries after one difficult pregnancy, and the result was that she had the horrible experience that was pregnancy #4? If so, she may fear that this is the only way she won’t get pregnant again because you’ll just blow off her concerns. (Not that you will, but she may feel that way.) If that’s at all the case, can you sit down and apologize for not dealing with this sooner, but reassure her that nothing will happen to her like that again?
She refuses counseling based on a single bad experience, she refuses to talk to a third party, she has set this ultimatum–is this typical behavior for her? Has she threatened divorce over other matters before?
It sounds as though she is acting out of a desperate, desperate terror of being pregnant again, rather like a trapped, hurt animal. Trapped animals aren’t rational–they’re just terrified. This is why I asked about PPD/PPA; she sounds as though she feels as though this is a life-or-death situation (which it is), and you’re asking her to die. What I’m trying to suggest is treating that trapped, wounded animal inside her: talk gently to her, tell her how much you love her, tell her that you, too, are worried about her health, that she’s safe, that you’ll work on this together, and that while there is no hurry, you also will put work in every. single. day. until you can figure out a solution together. At this point, postponing/ignoring this any further will do a LOT of harm, and will almost certainly lead to divorce. If she agrees just to wait a little, make sure to bring this, and what progress has been made, up frequently (like, daily or every other day) to reassure her that you are concerned about this too and that you’re working on it.
Has she actually talked to a NaPro doctor, or did she, like she did with suggestions about counseling, just decide it won’t work? Irregular cycles are one of the primary issues treated by NaPro docs.