Here's the page for the
Rodman DD-456 (destroyer) then hull number changed to DMS-21 when she was converted to a high speed minesweeper.
http://www.navsource.org/archives/05/456.htmHeres the page for the USS
Shea DD-750 (destroyer) later converted to DM-30 (minelayer).
If you check this site:
http://www.navsource.org/it will show you the majority of ships and craft in service in World War 2. Most of the YR craft were workshop and accomodation barges. Maybe your father was assigned to one working in a
Navy Yard or awaiting discharge? There is no record of a YR-45, maybe there was a mistake with the hull number on his records. Do his discharge papers or military record state where he was assigned to this craft?