Hot Baby has some level-headed council you'd do well to ponder. The truth of the matter is, this isn't the best of times to be rearing children anyway. Many couples are postponing parenting until their 30s and later. And if some reasons for this are positive [ex: women pursuing higher education], others are not. Socio-economic and political instability plus highly volatile international situations give intelligent couples significant grounds for waiting.
Unless your position is such that a pregnancy is a viable option for you [plural], it would be most unwise to proceed. And given such circumstances as I describe, I don't like the idea of your wife as your 'ex' raising this little one alone.
That said -- and if you're leveling with us -- you may not have much choice or say in the matter. You're a cuckold now. If her lover is influencing her toward a pregnancy skillfully, this may be as good as a 'done deal.' After all, birth control is very easily forgotten in the moment. Additionally, the risk of a pregnancy itself can be as hot as hell.
We don't know about your relationship with your wife. Does referencing you as 'Babydick' imply that she no longer thinks of you as her 'husband' or as a man? I can't be certain how serious she is about all this. Then again, maybe she isn't a particularly serious person. Maybe your marriage isn't particularly stable. Or maybe it is. I can't say. But you do need to broach these things with her. I suggest taking the best ideas presented here, print them out and use it as a basis of discussion with her.
You also made the comment that you're 'not convinced this is right.' Does this mean you're not sure it is a 'right idea?' Or, do you mean that you have moral issues in the sense that 'this is outright wrong and shouldn't be?' You must know your own mind on these things. And after that, there is the question of whether your general circumstances would support this decision. Then you can ask whether you really want this and are willing to agree with your wife for it to happen.
All the best!