What you are facing is nothing more than someone wants to have more children but feels the financial pressure of doing so.
When I get married, I probably would like to have at least 4 children, but I don't think I can afford that. So what will I do? Have two children at most.
Your hu*****and's first child is his blood. I understand you respect that, but I don't think you respect that enough.
Back to your question, I don't think you have a chance. In addition, brinig the issue up will put pressure on your hu*****and, which may not be good for your marriage.
The results of your situation will be very simple. You live with your decisions. You live with your budget.