A mouse is a 2D device. A 3D mouse is ... a 3D device. Another 3D device is ... a Joystick! Maybe the 3D mouse uses Microsoft's DirectX protocols. What happens if you run Acquire Input Data when your 3D mouse is connected? You may have to specify Joystick. You should also run DiagDx (the Microsoft DirectX Diagnostic routine and see if your 3D mouse shows up.
Now, if DiagDX shows the 3D mouse, there is a possibility that LabVIEW won't see it. There is a bug flaw in the LabVIEW routine -- it stops enumerating DirectX devices after 8 or 9, and can refuse to acknowledge higher numbered multi-axis devices. I've got a plea on the Idea Exchange here to ask NI to fix this, but not very many people have Kudo'ed (voted for) this Idea, so it hasn't (yet) been implemented. If this flaw bytes you, consider Kudo-ing my Idea (and tell your friends).
Bob Schor