Reduce a noisy 14vdc to 12v dc 3A with linear regulator or a switching regulator
To get rid of alternator 'whine' install a 300 uH to 1 mH or so inductor in series with your 12 volt power feed. It should be rated at twice the expected load current. 

This is one of those things where large capacitors are not enough. Back when I did car alarms and stereo's, an inductor was the best way to kill any alternator whine.

Grounding problems usually show up as odd radio or AC behavior, changing stations or volume by itself, blinkers coming on, dash lights flickering, etc.