I can't imagine an ethical quandary where the best answer is to brutally murder an innocent baby. I understand being an overtired mom (my wife and a I have 3 under 7), but every married woman I know uses birth control instead of making babies and murdering them. And one of ours we adopted from a family that already had 6 kids. I'm so grateful that her birth mother didn't think killing her would be better for her than to make an adoption plan.
I will definitely pray that your doctor will grant your wish to be sterilized.