Medicaid is a government program that is heavily regulated and there are no exceptions.
I would strongly suggest scheduling an appointment with the billing department at both your OBGYN and the hospital where you will deliver. If you tell them upfront that you will need to make payments they are more likely to work with you. You have 4 months to save $$$, so start pinching pennies.
Call the insurance company and find out exactly what their policy is. You say that you have to wait 6 months to get pregnant, but I think that means you have to be on their plan for six months before they will cover major expenses (very common). Many will work with you if you talk with an agent directly.
It is kind of silly for you to attempt to get a nanny job at this point... honestly I wouldn't hire someone who would need to take a leave within a few months AND who would need to bring her young children.
Worst case scenario, talk to the loan officer at your bank and see if you can take out a personal loan to cover the costs.
Be open and honest with the providers and see what they may be willing to do.