You cannot stay in US with the reason that your wife was pregnant even in case of your H1B denial.
You can apply for B1/B2 visa but changes of denial are very high as your H1B intent was for working in USA. I usually recommend against applying B1?B2 after h1B denial.
If baby is born in USA, he will get US citizenship irrespective of your status.
If you stay in USA after H1B denial for even 1 day, you will have to explain the reason for overstay in all future applications.