Here's a similar drum to your dad's old Ludwig and Ludwig. Looks like a '30s "super"...if it has a top snare mechanism it would be a "super sensitive." Bosth these drums in good original condition in regular nickel finish usuall bring $500-1000.
http://cgi.ebay.com/20s-LUDWIG-10-LUG-5X14-SUPER-LUDWIG-HEAVY-SNARE-DRUM_W0QQitemZ140145901410QQihZ004QQcategoryZ64434QQssPageNameZWDVWQQrdZ1QQcmdZViewItem
The top rim on yours is a modern replacement, but getting an original is easy.
That's the first Leedy and Ludwig I've ever seen like yours. I've seen some one off drums by that company, usually made for pros or endorsers. A forum member here, vadrums, I think has a similar 14" prototype Leedy Ludwig with offset lugs. Never saw those lugs before.
I'm thinking that even though it's a one of a kind, it wouldn't be worth tons of $. I'm guessing $350 to $600.
Drums by very famous drummers may bring in more, but usually it has to be Buddy or Gene (from that era). One of Sonny Greer's (Duke Ellington), 16 x 16 knob tension floor toms with "S / G" in blue sparkle over WMP got no bids at $900. (I bought it and sold it to a collector.) I've also received little interest in some Louie Bellson drums...
That Leedy and Ludwig is certainly a rare and special drum. You may want to take some photos of your dad with it, and also see if your dad has any photos of him in the studio. Thanks for posting those...