The part in that picture is an 18.75" 20ga barrel off of Remington's 870 Express Compact Jr.
http://www.remington.com
Pretty nifty little 870 actually. With an adjustable LoP stock and a magazine extension, it would make a nice HD piece that pretty much any member of the family could use effectively.
Barring discontinued parts or obscure aftermarket offerings, I don't believer a similar manufactured barrel exists for the 12ga, so you're probably relegated to custom pieces.
If you can't find an already-shortened one though, it's not all that complicated to cut a sporting-length vent-rib barrel down with a little know-how. You can find some great deals on those barrels in used condition. Some even have guide rings that are pre-drilled to accept a locking detent; a nice bonus if you can find one. Even if you need to have a gunsmith do some portion of the work, it would probably still be relatively easy on your wallet.
If you also want it threaded for choke tubes though, you'll have to find a specialty gunsmith with the right equipment.
