Uncontested divorce with problems in health care and paternity

It is not illegal for you to remove your wife from your health care plan unless there is a court order requiring that you maintain coverage until divorce is final.

If the wife is pregnant, the court may not delay the entry of dissolution; however, the court may reserve resolution of issues surrounding the unborn child, including determination of paternity and entry of a parenting plan or order of child support.

You are the presumed father of a child conceived while you are married. That presumption can be waived if the mother chooses and names another father. It sounds like she is not claiming that the child is yours.