What you describe sounds like after going to sleep the Mac is getting a wake signal from a USB device and assuming that your powered USB hub is powered correctly (e.g. it is tied to the ignition) then the GPS Mouse is your most likely culprit (though the touch screen *could* be too).
As far as coming back a few hours later and finding the Mini off, my first guess would be that it is the same problem. Sometime after it goes to sleep, the GPS mouse is waking it up. Then since your car is not on, the P1900 is cutting power to save your battery.
Pull everything that uses bus power off the Mac itself and make sure that it is powered based off the ignition line. Also check your powered hub as most now a days will use bus power if external power isn't present.