I do agree with everything you said about the desirabilities of AdvanceTrak. I do have a Track Pack car, and I have no need to turn off the nanny. It's my wife's daily driver.
It only goes off until you press the button again, or you turn the car off. It resets to fully on everytime you turn the car off. So unless you turned if off and then swapped seats with your wife without turning the car off, it will be on when she gets back in.
Also, performance tires turn to ice skates when you get below 50*. That is more than likely what you were experiencing and not advancetrak doing something strange.