1. What is her hu*****and's insurance. He should add her wife to the insurance. Of course, there will be additional cost.
2. If you do not have insurance. The only choice is emergency room when she really has problem or has to deliver. A bill will send to them later, but they can decide to pay it or not. If they plan to stay in US in future, then better to pay it.
3. If the child is born in US. The child will be US citizen, but if neither parent does not have green card, the Chinese government will not recognize the US citizenship, will issue a travel card to the child, instead of visa. It is tricky issue.
Good Luck!