I am sorry for your loss.
Your situation is too involved for an online answer. I suggest there is no standard form already customized to deal with your particular situation.
Using the written documentation from your father have is a good place to begin. Contact a local lawyer - many may give you a short free consultation - to discuss your specifics. Far too many variables exist in the short post you wrote for any further observation by me. Many attorneys have information posted here on Avvo.
You might find my Legal Guide helpful "How to Choose A Lawyer For You"
You might find my Legal Guide helpful " What Do I Tell My Lawyer"
No one can know what the record is in the case because online we cannot see your documents or the will. You need a lawyer. Check with a lawyer in your locale to discuss more of the details.
Good luck to you.
NOTE: This observation is made available by the lawyer for educational purposes only. This observation is not like a communication with a lawyer with whom you have an attorney-client relationship along with all the privileges that relationship provides.
You can review my Avvo Legal Guide on the release of adoption records in Virginia. You can try to obtain records from the Virginia Department of Human Services.
If he named you in the Will, did he not state your name? If so, you should not need the birth certificate.