What a tough situation. Are you in marriage counseling? If not, I think both marriage and individual counseling needs to be a priority. The bottom line is she either needs to start learning to trust again and move forward or end the relationship. But continuing to punish you gets neither of you anywhere.

I am generally of the mind that once done having children, the men should have the surgery since it's much simpler and the women have had to endure far worse through pregnancy. However, no one should be forced to endure a surgery they don't want. It's like you asking her to have plastic surgery to be more attracted to her. You have to want to do it for yourself. I'm wondering if this is just an excuse for her and if you have the surgery if she will then come up with some other reason not to be physical with you.

If things don't work out with your wife, would you want more children in the future with someone else? If not, and you are totally done having children no matter what, then I think you should do the surgery. It's a routine surgery and recovery is one or two days.

Good luck!