Indeed, how did it get so bloody complicated? JoeKan asks a simple question and it spirals out of control.
While kindly offering his advice to JoeKan, Vic happened to mention an issue with Toyota alternator outputs. I have a Tacoma with 130A alternator and have never been happy with its ability to charge the camper battery, even after driving all day, let alone the half hour that you propose. Vic suggested two main solutions to my problem (bigger wires and/or a DC-DC charger) and others have added good advice, including pvstoy's well-justified admonition to install a good battery monitor and learn to use it effectively.
So, thanks to everyone's input, I think I have a solution that will allow me to use the truck alternator exactly as you suggest. But, who ever said life was meant to be easy?