I believe it is an RF issue.
If your alternator is a standard style alternator you should be able to remove it and have it tested. If it is an issue then it is likely too small for your application unless you have a Diode that went bad so its "sort" of working but only at half output. The battery is taking up the slack. One note is that if a diode does go bad I have heard of it causing extra RF issues. But like I said, you can easily have it checked out if you suspect a bad alternator.
My suggestion is to temporarily place a battery in your car to run the mac mini setup on a power system separate from your car. This is only for testing purposes to identify if it indeed is something in your charging system causing the issue. One you try it and find out either way you can remove the battery and go from there.
I am no expert at shielding against RF but if you read the thread about shielding an M4-ATX you will be well on your way. Those power supplies are known to have issues with RF.
I don't know if you will be able to fully filter out the RF easily however if this is the issue. Since you have to have the screen available it can not be shielded...