The best and easiest way to get what you are asking about is to run a line level converter off the stock head unit and into the amp using y connections, it would look like this using your drawing.
Stock head unit->Line level converter->
Carpc --> Optical / digital converter --> good amp --> pioneer PRO speakers via THICK speaker wires
It will play both if you leave both on but it won't be bad for the system as long as both are not turned all of the way up, just annoying. In the same manner you could go line level into the computer and route it that way too, not the way I would do it since the head unit is available nearly instantly and it takes time for the car pc to boot, but you could is more the point. I hope this helps some.