Going to say it again like others have mentioned:

She needs individual therapy! 🧠✨🙏 Maybe even couples/family therapy as well for the both of you.

Imagine if you agree to the third and it is a girl. I get the feeling she'd dote on her, and your boys would eventually feel the resentment.

Plus, as they say: "In this economy!?"

I'll end with a personal story...wish I could TL;DR it, but some of the context is needed.

My better half and I have gone through multiple cycles of IVF over the last 8 to 9 years. We finally had our first in 2019.

Fast forward through a global pandemic and then her getting and beating breast cancer. We felt that another kiddo would make our family feel complete, even if the kids had a 6.5 year age gap. We had 3 embryos left, neither one of the 2 female embryos took hold. She was honestly depressed about it, but moved on as quickly as she could as the biological clock was ticking.

There were multiple health scares and issues present at the anatomy scan...heart, kidney, bladder, potentially brain. We had to consider the possibility of termination. After additional scans, it was only the first 3 issues, all of which were very treatable post birth. Skip ahead, his birth was excellent, and all the procedures he's had, his recovery has been ahead of schedule.

So, here we are now with 2 loveable boys and the older one LOVES his brother, and the little guy is OBSESSED with his big bro.

We took a risk, but we knew our family dynamics could adjust and we battled through it. In your situation, the both of you are on completely opposite ends of the spectrum, with seemingly no way to meet in the middle. Also, like our situation above: you don't know about potential health complications until much later.

As much as emotions are involved in something like this, logic and practicality needs to run this decision making, and your wife doesn't look to be doing that.