She really said something like that?! Sounds like trouble...
I don't think it's fair to resent someone because they are incapable of having children. Are there literally health reasons or does she just hate the idea? She already has 4 kids. She probably isn't interested in having another. Understandable. Four kids is a lot, but I think compromise here is important. I would suggest maybe seeing a doctor with her and getting an opinion about it.

I will say that reading that statement about her saying something about breaking up so you could find someone else leaves a bad taste in my mouth. Really? Who says something like that to someone they want to spend their life with? Was that comment driven by insecurity, guilt... lack of care?...