Meet with the judge at your scheduled date and explain your reason for wanting the adoption records unsealed. Generally, you will have a better chance if your reasoning isn't based solely on personal desire or interest. Medical issues are the most common reason sealed adoption records are unsealed. However, you can consult an adoption lawyer to build the best argument no matter what your reasoning. The judge will either grant your petition and unseal the records or deny your petition. If this happens, you can request a confidential intermediary.
In all adoption searches, it is uncommon to find both the birth mother and father at the same time. A separate search, if desired, can be done afterwards for the father. Since males seldom change their surnames, and the mother might have additional information, it is usually easier than the initial search for the birth mother. In many cases, adoptees are able to do this second search for their birth father by themselves (or they try before paying for assistance).