Me [36M] with my Wife [34F] married 12 years, 4 kids (have girls and a boy). Wife wants 1 more, I really don't. I am interested in getting Vasectomy, but she "won't allow it". How to best navigate?

Generally good marriage. We can both be stubborn, so compromise doesn't come easy (especially for DW, who is very religious - I am not).
We are at an uncomfortable stalemate. She comes from a family with 5 kids, I have only one other sibling. She feels there is a "hole" in our family and that 5 kids is the perfect number. I do not want any more and feel 4 is already a large family.
Her reasons for wanting another:

• She feels there is a "hole" still in our family
  
• Being a mother is her most rewarding life experience (she doesn't work full-time)
  
• She loved having several siblings and feels the more the better
  
• I believe she loves the baby/toddler phase, which has been present in our house for the majority of our marriage.
  

My reasons for not wanting more children:

• I am completely satisfied with our 4 children and don't want to dilute my time and attention any more than it is with them
  
• I would like to retire early and more kids means I'm working more years
  
• DW has expressed interest in going back to work, but only after all kids are in full-day school, having another would reset the clock
  
• DW is very religious and insists on raising the children in mormonism. I have left the church and it pains me to see my children indoctrinated so young.
  

Aside from having more kids, her libido impacted by birth control. I'm supportive of her going off birth control, but I mentioned that this may mean I don't ejaculate inside of her, even with a condom. She would never consider an abortion, so if she accidentally gets pregnant we would essentially have another kid. For some reason she doesn't like me not finishing inside her. I mentioned I could look into a vasectomy and it was a hard no for her (she feels like that's me making a final decision for her since she still holds out hope that I may reconsider sometime in the future).
I feel sort of stuck. In a way, I should be able to get a vasectomy with or without her approval, but don't want to upset her. I am now concerned that the birth control issue will negatively impact our reasonably good sex life. Any thoughts?

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tl;dr: Wife wants a kid, I don't. Wife wants to get off birth control, but isn't supportive of a vasectomy. Any advice?


Source.

Prayers sent lol