Stereo Hums when grounded to frame

Ok I isolated to where my noise is coming from.  I have 0 hum if my stereo is only grounded threw the stereo's ground wire.  But as soon as there is a ground on the frame it hums.  At the moment it hums only when its screwed in.  Do any of you know a trick to isolate this. 

Ok I understand im introducing a grounding loop.  Here is the issue now though.  I get lower resistance to the negative terminal on the battery, because its an mr2 and the battery is closer to the reciever.  This is why i get a grounding loop because the ground on the rca have a lower resistance than the ground at the amplifier, do to distance.   

My next move im going to do, check the frame ground, relocate the amp grounds( better spot) then try it agian.