Let me pose a contrarian view: how would you like it if your husband imposed his religious rules on you? Without knowing what, if any, his religion is, let me ask if he came home and said he could no longer live in a home where a crucifix was displayed or be near a woman who wore Saint’s medals how would you feel?
I don’t think she’s talking about saying she couldn’t live in a home with a man who had a vasectomy. She’s saying that he needs to know ALL the effects his vasectomy is likely to have, including effects on his relationship with her. She can also tell him what she will do to mitigate those effects, and what the cost to her personally will be.
I don’t think saying “If you love me, you won’t do this” makes sense - he probably honestly believes this is the best thing for both of them, and his goals (which might be things like not bring more stress into the relationship w/ another child, preserving their sexual relationship, etc.) should be recognized for those parts which are good.
However, the OP
can have this conversation without blackmail. Expect him to feel defensive, though, and sprinkle the conversation with reminders that you love him and want to get through this
together, whatever his decision is. You married him for better or worse, and that means trying to make the relationship work no matter what - and you know that, but make sure
he realizes that you know that and that your relationship is
not on the line. Your happiness for a while might be, though, and if so, he deserves to know that. He also deserves to know that this might affect your attitude towards sex, even though you
want to preserve your sexual relationship no matter what, and that sex might be emotionally uncomfortable and a real sacrifice for you for a while (if that is how you feel).
Go in to the conversation knowing that you want him to change his mind, but will not force him to. Let him know that if he won’t change his mind, then you want him to help you come up with a plan to cope with these fears and feelings
together, because they are real and they may affect you both much worse if they are ignored - and let him know that you don’t
want to hold on to them, but may need his help to overcome them. Make yourself vulnerable, and trust in your DH and God with love.
If you aren’t open with him, you may find yourself unable to enjoy relations with him and he may not know why. Imagine how much more painful this discussion will be if you wait. He may feel betrayed that you didn’t trust him enough to tell him these things, or upset anyways because he may
still feel black-mailed. Worse, there is nothing he could do if you wait. If you tell him now, you can give him the chance to sacrifice for you without forcing the issue - and he might honestly prefer that. Don’t make his choices for him by withholding this information.
Try and figure out how to open the conversation so that he will hear that your relationship is not on the line, and keep the message “I love you and want to share the rest of my life with you, no matter what” always in the background. Whatever ideas you come up with, make sure you each try to understand what the cost to the other will be, and both also realize that your partner deserves to understand what you are sacrificing as well. If the conversation goes poorly, feel free to suggest dropping it and picking it up later when you are both calmer again. You guys want to make the best decision about this that you can, and it
is a big decision. If he doesn’t want you to be a part of his decision or shuts you out in some other way, draw close to your DH through God by praying for him. If he is willing to talk with you, say “Thank you” for his own openess and honesty even if you don’t like what you hear.
Also, consider speaking with a priest about what you are going through. Pray for your husband not to have this surgery, and that whatever comes, God will give you what you need to be a light to your beloved. If you can, pray before any conversations with him.
BTW, these are just my thoughts. If anything doesn’t seem to apply to your situation, please throw it out. You are in the situation, and your judgement on the situation will be better than anyone on this forum.
Prayers for you and your DH.
Don’t underestmate God! He can accomplish anything even when we humans put “limitations” on what we think He can do. I even have heard of couples that have gotten pregnant when she had her tubes tied and he had a vasectomy.