Dear Martha Finfrock:
Thank you for posting on History Hub!
You may be able to locate the father’s naturalization record by contacting U.S. Citizenship and Immigration Services (USCIS), who holds naturalization records since September 27, 1906. Here is a link to their Genealogy webpage. I am not sure if an application form was required to obtain a Certificate of Arrival. But USCIS can determine if a C-File exists, which may include the Certificate of Arrival.
You can also request the mother’s and daughter’s C-File, the C-File may contain the same naturalization records you already have, but could contain more.