Is my ex-wife required by law to update my daughter's Social Security information if my daughter's name has been changed legally?

I recently had my daughter's last name changed, however, even though it was court ordered and all that, the ex wife is not only mad, but spiteful. Altough I said otherwise, she stated that she is not required by law to change her social security card. Now, I would go do it myself, but I tried that, and they told me that they needed shot records to show my daughter's alive and well. I'm not sure if the court order would suffice, but still. I was hoping that once my ex saw the birth certificate, she would realize I wasn't joking and just go get it updated.