You have to set the bar to mode 4, then, once you start dolphin, you go to the wiimote configuration menu, there should be an area for a "real wiimote" (instead of entering the "emulated wiimote menu") You just have to press "refresh" and / or "pair up". The wiimote should rumble once, indicating that it has been paired up with the emulator and therefor there is no need to configure anything else: it will behave like it would on a real wii. Tested it with "New Super Mario Bros Wii" and it worked like a charm.
Regarding a list of on rails shooter games that can be used with the dolphinbar, either as a mouse emulating device (mode 2) or within Dolphin (mode 4), here are the games I could come up with so far, of course some of them have several ports available, but I avoided those if I managed to get the original one to work fine, or in favor of the best / easiest to run version (like THOTD overkill, which is available on wii, but has a superior PC port):
On Supermodel (obviously):
-The Lost World
-The Ocean Hunter
-L.A. Machineguns
-Star Wars Trilogy
On model 2 emulator:
-Virtua Cop
-Virtua Cop 2
-The House of the Dead
-N.Y. Machineguns
On MAME:
-Lethal Enforcers
-Area 51
-Hogan's Alley
-Duck Hunt
-Wild Gunman (if you get it to work, that is. The NES version is roughly the same, though)
-Alien 3 The Gun (need to set the analog input to mouse movements)
-Jurassic Park (same as Alien 3, insanely hard, though)
-Crypt Killer (Psx version available in case your CPU is enough)
-Time Crisis (needs beefy CPU, PSX version is pretty good though)
-Point Blank (same as the above)
On PC:
(Haven't actually tried these, but I don't see any reason why they shouldn't work)
-The House of the Dead 2
-The House of the Dead 3 (pretty decent port, runs better than the wii version)
-The House of the Dead Overkill (it is included in the PC version of The Typing of the Dead Overkill from the get go)
-Rambo The Videogame (wanted to try the bar with it, but it crashed on boot up. I guess it's a drivers issue, as I completed the game before on this same PC)
(There are also PC ports of both Virtua Cop titles and HOTD, but they are based on the Saturn versions and, given that the originals look way better on Model 2 emu, there's little to no reason to pick these above the originals. Virtua Cop 2 has an extra area in the subway, though)
On Dolphin:
-The House of the Dead 2&3 return (HOTD2 is actually a better port than the PC one)
-Ghost Squad
-Resident Evil: The Umbrella Chronicles
-Resident Evil: The Darkside Chronicles
-Dead Space Extraction
-Links Crossbow training
-Target: Terror
On Pcsx2:
(Most of these games require that a virtual guncon or a virtual mouse be set up via nuvee ps2 usb plugin, which might be a little cumbersome to configure, specially in regards to calibration. The upside is that there's lots of games of the genre on the system)
-Vampire Night
-Time Crisis II
-Time Crisis 3
-Crisis Zone
-Ninja Assault
-Virtua Cop Elite Edition (a remaster of shorts of the first two Virtua Cop games, I find it a bit uninspired on the visual department when compared to the colorful originals)
-Gunfighter II: Revenge of Jesse James
-Endgame
-Police 24/7
-Resident Evil Gun Survivor 2 (although I prefer playing this with a Dual Shock using "Type E" controls)
-Dino Stalker (Fun game but somewhat cumbersome to control)
-Resident Evil Dead Aim (easier to control using a controller and a USB mouse than the Guncon, actually)
Those are the ones I can come up with. I'm sure there are many others.