Just an educated guess, but I think you may talk to these devices via Windows, not by communicating directly with their driver. They should be under Control Panel > Game Controllers (if using Windows XP, at least).
If, for example, you wanted to receive data from the mouse or send data to the speakers, you don't talk directly to the device's driver - instead, you talk through Windows, because it is "owned" by Windows. I think the same may apply to a joystick.
Having said that, if this is a fancy force feedback joystick then Windows may not support it and you may need to talk directly to its driver.
Just a pointer - you may need to talk to Windows APIs, not the device drivers. I don't know how though, but I hope this points you in a direction.
If there is not a ActiveX control, have you looked into DirectX, which includes directInput an API for controlling input devices mostly for gaming. I haven't had to use it in the past but have looked into it for the possibility of adding joystick control to LV programs. I don't know if your device is compatible with the directInput API however, but it is worth investigating since directInput supports forced feedback. MSDN has good documentation on using the API. Good Luck
Like Paul or Sean suggested, using directX, win API, or DLL calls can all provide a solution to your problem.
I would suggest looking at http://digital.ni.com/public.nsf/websearch/CA411647F224787B86256DD000669EFE?OpenDocument for some more information on reading the joystick/gamepad. To send the force feedback, I would suggest trying to find some more information on the driver provided with Logitech device (maybe searching on google forums) and then calling the functions in LV.
If you end up using the dll's then you can use DependencyWalker (not an NI utility) to get the function names in that dll and then probably searching web on those function names.
You are working on a cool application and maybe you are the first one doing it, so do post the solution in the end.