I moved this to its own thread in order to keep the other one focused.
To answer your question, GPS Navigation systems are not tied into the trip odometer in any way. This is for the standalone setups, factory setups, or the PCs we install into our rides. It won't reset the trip odometer and it won't communicate witht he trip odometer in any way.
Some GPS navigation systems have the ability to save and/or recall a route, but that is a function of the navigation software itself.
If yu're paranoid about your spouse tracking you, there's a simple solution: reset the trip odometer when you get out of the car. Granted, if you're going places you're not supposed to, he could always look at the main odomoeter and do some simple math.
Frankly, if you suspect your spouse of spying on you, then you need to confront that issue with your spouse rather than trying to counterspy on him or figure out his tactics.