I wish social workers would refrain from practicing immigration law. As a matter of basic fairness, why should visitors, who have never paid income taxes or property taxes, have their childbirth covered by Medicaid? You are quite correct that using Medicaid could affect your future visa applications. When you have already been on public assistance as visitors to the USA, it is harder to prove that you will be self-sufficient if you are allowed to immigrate here. Pay for the birth yourselves and maintain your integrity.
Answer Applies to: Washington
You are correct. Be careful when using Federal Benefits that could be used against any future petitions with you and your wife. The Medicaid is meant for your child, who is a U.S. Citizen. If you have the means to pay for the hospital care and birth, I would advise that you do so. The questions of whether you have ever used or have been a recipient of any government benefits is a question in all immigration forms.
Answer Applies to: Texas
I see no reason why it should affect her future visa application. Legally, you are on solid ground. Medicaid covers visiting relatives of those who pay for it, in this case your wife's family and perhaps yourself as well. Morally, I am sure you will do the right thing for you and your family and I do not know what that is. Good luck!
Answer Applies to: California