Hi there,
This is certainly my field of expertise so I will take this one.
NGUI and Vuforia certainly aren't friends out of the box... and this is more to do with how AR camera works rather than NGUI so you may be better asking on the vuforia forum instead... however I use vuforia every day at work so I will do my best.
What you are trying to do is use 2 main cameras which is not advisable. First of all the AR camera is the big boy in the project and must remain the main camera. You could then remove the NGUI camera from the UI and place it under the AR camera, You will then need attach the attached script to the NGUI camera and drag the AR camera onto that script in the inspector. Then go back to your UI and disable the anchor (no need to delete it).
Make sure your UI is on the GUI layer, and that the AR camera is ignoring that layer. Then make sure the NGUI camera is only rendering the GUI layer.
You must also make sure that the UI is a 3d ui and not 2d it must be 3d to work with vuforia.
Finally make sure your camera is set to 0, 0, 0 in positioning, as it needs to follow the AR camera exactly. The NGUI camera must also have the same clipping and field of view settings as the AR camera.
Sorry that this was written so long winded but I am really busy and had to rush. Hope this helps and let me know if you get stuck or ask in the Vuforia forums
