Possible CRM nightmare scenerio here....

I do think keeping inside the cockpit at this point is warrented. You have made 2 attempts to fix this issue, one very reasonable, the other a quick shouting episode (needed). I do think another sit down over a beer or 2 should occur before the next flight (within regs of course). Then if it happens one more time in flight, you have a couple options, it is his plane, so give him controls at all times, and turn the intercom off. Or you keep the controls, and tell him you are turning the radios off (don't actually do it), that could force him to pay attention. Remember its his plane, his flight violation for missing radio calls/instructions. Now I realize this is somewhat outside the box, but this guy needs fixing, and no one wants to be the "rat" if they don't have too.

Overall point here, give it one more shot before going outside the cockpit.

And good luck, you should not have to deal with BS like this.