Remember the vow about freely welcoming children? God's will. Not your lifestyle or at your convenience.
Start breaking the vows you end up breaking the marriage, talk to a priest, both of you.
But it sounds like already your communication has broken down. Work fast.
I agree, if it means the breakdown of my marriage I don't see a way out...anone hve experience with the following, Popular types of natural family planning include the rhythm method, and the basal body temperature method.
My advice is bribe her to meet NOT A PRIEST but a married couple of about your age, or a few years older, who live in a beautifully tidy house and talk to couples about natural family planning. Women want to hear this stuff from women basically. If she is a bookworm there are so really well written and funny books on the topic too. You can find counselling couples like this through the NFP associations.
When she is a little happier with the concept then you can see a priest.