Hi
The record office near to Alfriston would be a good starting point, they may well have a licensd vitular book, if this book has survived and been handed in it will list the person that owned the public house.
Perhaps the father owned the public house but didn't run the business himself? This might explain why he is not listed in the trade directory.
Contact east Sussex record office and ask if they one and give the name and dates you are interested in - they may look for you.
The pub may have changed hands serveral times and been taken up by a bigger brewery, which could mean that the original deeds have gotten lost on the way (this often happens unfortunately) - this may be why the silence when you contacted them before.
Lemon