The White balance will be accurate as long as the gray is not also over-exposed. If the Gray is OE than the WB is useless.
The problem is that you are overexposing the WhiBal card shot. You can see that the White Bar is almost indistinguishably from the gray of the card. Once you overexpose the card like this the White Balance information carried by the WhiBal shot is lost, and that is why the colors will be bad. Some of the color channels (RGB) are being clipped which alters their ratio which is how WhiBal works.
The WhiBal shot does not have to be at the same exposure as the other shots, just the same light.
A good guide to a proper WhiBal exposure is to make sure that the Whiter Bar on the card is not "blinking" on the back LCD of the camera.
Hope this helps..
BTW...Your wife is very pretty. She deserves proper color balance :>)
Please feel free to post again when you have toned down the WhiBal exposure.
Should I hold the whi-bal with the top part facing the sun (horizontal to the floor) or the top part facing the camera (vertical to the floor)?
Parallel to her face, perpendicular to the ground, parallel to the camera sensor (film plane). This does not have to be precise, but that is the orientation. Also use the black and white puddles to check for glare off the card which should be avoided as well.