Birth of a Newborn – Care Billed to Spouse’s Plan

My wife and I both have insurance policies through our employers. We recently had a newborn. We decided it would be best to put our newborn child on my health insurance during the 30 day special enrollment period as it is a cheaper premium and includes better coverage. The hospital never asked us for the insurance we would be using for the newborn, rather they are billing all newborn charges to my wife’s insurance since she delivered the baby. The problem is we don’t plan on adding our newborn to this policy and we are now getting explanations of benefits showing processed claims for the newborn on the wrong insurance. For example, our newborn was billed $9,400 for inpatient services and room and board, my wife’s policy discounted the claim to $4180, insurance paid the hospital $3340 and stating we owe the hospital $840.

How would you proceed to ensure the medical claims are being processed through my insurance and not my spouses for our newborn’s care? Since my wife’s insurance policy already paid out the hospital, would we get a bill in the mail from the insurance to pay this back once they discover we did not add the newborn to her policy after 30 days? Should we call her insurance, the hospital, my insurance or a combination to resolve this? What is the right way to handle this situation?